7-blocks with elementary abelian noncyclic defect group in the ATLAS groups:

Block information:

• k(B),l(B) invariants.
• Principal block of local subgroup, where relevant.
• Diagonal of Cartan matrix when the decomposition matrix is known or conjectured (marked with *).
• Degrees of irreducible characters, divided by gcd.
• In some cases, the generalized decomposition matrix.
  KEY to links between blocks:
  • IN: Inflation
  • CL: Clifford theory
  • MU: Direct Product
  • MO: Morita Theorem
  • ISO: Isomorphic
  • SC : Morita equivalence related to Scopes reduction
  • references to proven cases, [Oku1],[Hol] etc.,can be found on Jeremy Rickard's Abelian Defect page:
    http://www.maths,bris.ac.uk/~majcr/adgc/adgc.html or at the bottom of this page.
    The database contains 98 blocks.
    Documentation

k(B) = 16, l(B) = 12

• (C7XC7):C127-block 1
  

• [ ]

  • 2.L2(49).2_2 7 -block 4, [ 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25 ]
    
    

k(B) = 17, l(B) = 7

• (C7XC7):Q8:C37-block 1
  

• [ 5, 8, 8, 8, 8, 11, 12 ]

  • 3D4(2) 7 -block 1, [ 1, 26, 52, 324, 351, 351, 351, 468, 1053, 1664, 2106, 2106, 2106, 2808, 2808, 2808, 4096 ]
    
    

k(B) = 19, l(B) = 6

• (C7XC7):D127-block 1
  

• [ 8, 8, 8, 8, 17, 17 ]

  • L3(8).2 7 -block 1, [ 1, 1, 72, 72, 146, 146, 146, 512, 512, 657, 657, 657, 657, 657, 657, 1168, 1168, 1168, 1314 ]
    
    

k(B) = 19, l(B) = 7

• (C7XC7):D167-block 1
  

• [ ]

  • 2F4(8) 7 -block 1, [ 1, 1839048, 201301200, 461921616, 545261600, 1210323465, 1210323465, 1210323465, 7532740608, 8741225025, 8741225025, 8741225025, 68719476736, 69929800200, 69929800200, 69929800200, 77460701760, 77460701760, 77460701760 ]
    
    

k(B) = 20, l(B) = 3

• (C7XC7):S37-block 1
  

• [ 12, 12, 33 ]

  • L3(8) 7 -block 1, [ 1, 72, 73, 73, 73, 73, 73, 73, 512, 584, 584, 584, 584, 584, 584, 657, 657, 657, 657, 657 ]
    
    

k(B) = 20, l(B) = 9

• (C7XC7):S3XC37-block 1
  

• [ 3, 4, 4, 4, 4, 6, 6, 6, 7 ]

  • L6(2) 7 -block 1, [ 1, 62, 744, 1240, 1395, 1395, 4185, 4185, 5952, 6480, 9920, 11160, 11160, 12555, 25110, 25110, 31744, 32768, 33480, 33480 ]
    
    

• [ 6, 6, 6, 6, 6, 6, 13, 13, 13 ]

  
  
  • L3(8).3 7 -block 1, [ 1, 1, 1, 72, 72, 72, 219, 219, 512, 512, 512, 657, 657, 657, 657, 657, 657, 1752, 1752, 1971 ]
    
    

• [ ]

  
  
  • P1L72 7 -block 1, [ 1, 62, 744, 1240, 1395, 1395, 4185, 4185, 5952, 6480, 9920, 11160, 11160, 12555, 25110, 25110, 31744, 32768, 33480, 33480 ]
    
  • P1L82 7 -block 15, [ 1, 62, 744, 1240, 1395, 1395, 4185, 4185, 5952, 6480, 9920, 11160, 11160, 12555, 25110, 25110, 31744, 32768, 33480, 33480 ]
    
  • P2L82 7 -block 1, [ 1, 62, 744, 1240, 1395, 1395, 4185, 4185, 5952, 6480, 9920, 11160, 11160, 12555, 25110, 25110, 31744, 32768, 33480, 33480 ]
    
  • P2L82 7 -block 2, [ 1, 62, 744, 1240, 1395, 1395, 4185, 4185, 5952, 6480, 9920, 11160, 11160, 12555, 25110, 25110, 31744, 32768, 33480, 33480 ]
    
  • P2L82 7 -block 3, [ 1, 62, 744, 1240, 1395, 1395, 4185, 4185, 5952, 6480, 9920, 11160, 11160, 12555, 25110, 25110, 31744, 32768, 33480, 33480 ]
    
  • L7(2) 7 -block 1, [ 1, 2540, 9144, 35433, 35433, 62992, 89280, 177165, 177165, 503936, 585216, 708660, 708660, 1300480, 1417320, 1417320, 1594485, 2097152, 2267712, 2267712 ]
    
  • P1L82 7 -block 1, [ 1, 2540, 9144, 35433, 35433, 62992, 89280, 177165, 177165, 503936, 585216, 708660, 708660, 1300480, 1417320, 1417320, 1594485, 2097152, 2267712, 2267712 ]
    
    

k(B) = 22, l(B) = 18

• (C7XC7):GQ12XC37-block 1
  

• [ ]

  • A14 7 -block 1, [ 1, 13, 78, 286, 429, 715, 1287, 1716, 4576, 4752, 4752, 6435, 15444, 21450, 21450, 24960, 29952, 29952, 34320, 34320, 36608, 69498 ]
    
  • A15 7 -block 1, [ 1, 90, 715, 1430, 1716, 1716, 2925, 7722, 11583, 14300, 19305, 21450, 35100, 44550, 53625, 78000, 78000, 96525, 128700, 146432, 146432, 231660 ]
    
  • A17 7 -block 2, [ 16, 544, 4862, 6435, 6435, 20400, 116688, 159120, 233376, 243100, 353600, 583440, 583440, 631125, 631125, 700128, 729300, 729300, 908820, 972400, 1050192, 1326000 ]
    
    

k(B) = 22, l(B) = 21

.. ..


• [ ]

  • L2(49).2_3 7 -block 1, [ 1, 1, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 96, 96, 96, 96, 96, 96, 100, 100, 100 ]
    
    

k(B) = 25, l(B) = 9

• (C7XC7):C3XC37-block 1
  

• [ ]

  • 7:3xpsl(3,2) 7 -block 1, [ 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 8, 8, 8, 9, 9, 9, 9, 18, 18, 24, 24 ]
    
  • P3L62 7 -block 1, [ 1, 3, 3, 3, 3, 6, 6, 8, 8, 9, 9, 9, 9, 18, 18, 18, 18, 24, 24, 24, 24, 36, 48, 48, 64 ]
    
  • P3L72 7 -block 1, [ 1, 3, 3, 6, 8, 20, 45, 45, 60, 60, 64, 120, 135, 135, 135, 135, 160, 192, 192, 270, 270, 360, 360, 384, 512 ]
    
    

k(B) = 25, l(B) = 18

• (C7XC7):S3XC67-block 1
  

• [ 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7 ]

  • L3(8).6 7 -block 1, [ 1, 1, 1, 1, 1, 1, 72, 72, 72, 72, 72, 72, 438, 512, 512, 512, 512, 512, 512, 1314, 1314, 1314, 1971, 1971, 3504 ]
    
    

• [ ]

  
  
  • L6(2).2 7 -block 1, [ 1, 1, 62, 62, 744, 744, 1240, 1240, 2790, 5952, 5952, 6480, 6480, 8370, 9920, 9920, 12555, 12555, 22320, 31744, 31744, 32768, 32768, 50220, 66960 ]
    
  • L7(2).2 7 -block 1, [ 1, 1, 2540, 2540, 9144, 9144, 62992, 62992, 70866, 89280, 89280, 354330, 503936, 503936, 585216, 585216, 1300480, 1300480, 1417320, 1594485, 1594485, 2097152, 2097152, 2834640, 4535424 ]
    
    

k(B) = 25, l(B) = 21

.. ..


• [ ]

  • 2.L2(49).2_2 7 -block 1, [ 1, 1, 25, 25, 25, 25, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 96, 96, 96, 96, 96, 96, 100, 100, 100 ]
    
  • L2(49).2_2 7 -block 1, [ 1, 1, 25, 25, 25, 25, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 96, 96, 96, 96, 96, 96, 100, 100, 100 ]
    
    

k(B) = 26, l(B) = 18

• (C7XC7):C2XC3XC37-block 1
  

• [ ]

  • (A7xL2(7)):2 7 -block 1, [ 1, 1, 6, 6, 6, 6, 6, 8, 8, 15, 15, 20, 36, 36, 36, 48, 48, 60, 60, 90, 90, 90, 120, 120, 120, 160 ]
    
    

k(B) = 26, l(B) = 24

• (C7XC7):C247-block 1
  

• [ ]

  • 2.L2(49) 7 -block 1, [ 1, 25, 25, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50 ]
    
  • L2(49) 7 -block 1, [ 1, 25, 25, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50 ]
    
  • 2.L2(49) 7 -block 3, [ 12, 12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25 ]
    
    

k(B) = 27, l(B) = 21

• (C7XC7):(SL23XC3)7-block 1
  

• [ 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7 ]

  • 7^2:(3x2A4) 7 -block 1, [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 24, 24, 24, 24, 24, 24 ]
    
    

• [ 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6 ]

  
  
  • 2.Co1 7 -block 46, [ 3, 253, 572, 5060, 11960, 37375, 39468, 98670, 242190, 631488, 888030, 1144000, 1144000, 1644500, 2131272, 2466750, 4269375, 6166875, 6314880, 8419840, 26312000, 26943488, 39190528, 49335000, 60720000, 64737387, 81920000 ]
    
    

• [ 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6 ]

  
  
  • 2.F4(2) 7 -block 58, [ 13, 5525, 11700, 13770, 13770, 106080, 106080, 141440, 143208, 143208, 179010, 179010, 397800, 397800, 1342575, 1342575, 1432080, 1432080, 1718496, 1718496, 2263040, 2386800, 2864160, 2864160, 3790800, 3790800, 4194304 ]
    
    

• [ 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5 ]

  
  
  • 2.Co1 7 -block 1, [ 1, 276, 299, 17250, 80730, 94875, 822250, 871884, 1821600, 2055625, 9221850, 16347825, 21528000, 21579129, 24667500, 31574400, 57544344, 66602250, 85250880, 150732800, 163478250, 191102976, 207491625, 215547904, 219648000, 299710125, 326956500 ]
    
  • Co1 7 -block 1, [ 1, 276, 299, 17250, 80730, 94875, 822250, 871884, 1821600, 2055625, 9221850, 16347825, 21528000, 21579129, 24667500, 31574400, 57544344, 66602250, 85250880, 150732800, 163478250, 191102976, 207491625, 215547904, 219648000, 299710125, 326956500 ]
    
    

• [ 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6 ]

  
  
  • 3D4(2).3 7 -block 1, [ 1, 1, 1, 26, 26, 26, 52, 52, 52, 324, 324, 324, 468, 468, 468, 1053, 1053, 1053, 1053, 1664, 1664, 1664, 4096, 4096, 4096, 6318, 8424 ]
    
    

• [ 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9 ]

  
  
  • 2.F4(2) 7 -block 1, [ 1, 1105, 1105, 1326, 1377, 44200, 44200, 99450, 99450, 183600, 183600, 322218, 358020, 358020, 947700, 1342575, 1342575, 2828800, 2828800, 4526080, 4526080, 5640192, 8055450, 8055450, 10740600, 10740600, 16777216 ]
    
  • F4(2) 7 -block 1, [ 1, 1105, 1105, 1326, 1377, 44200, 44200, 99450, 99450, 183600, 183600, 322218, 358020, 358020, 947700, 1342575, 1342575, 2828800, 2828800, 4526080, 4526080, 5640192, 8055450, 8055450, 10740600, 10740600, 16777216 ]
    
    

• [ ]

  
  
  • 2.2E6(2) 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2.2E6(2).2 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2.2E6(2).2 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2) 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).2 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).2 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).3 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).3 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).3 7 -block 3, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).3.2 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).3.2 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2E6(2).3.2 7 -block 3, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2) 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).2 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).2 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).3 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).3 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).3 7 -block 3, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).3.2 7 -block 1, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).3.2 7 -block 2, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2^2.2E6(2).3.2 7 -block 3, [ 1, 1938, 48620, 554268, 815100, 1828332, 2956096, 20155200, 22170720, 145411200, 145411200, 221707200, 497306304, 505076715, 1289932800, 1418926080, 2270281728, 3338649600, 7488847872, 7576150725, 10101534300, 12745441280, 32324909760, 32514244608, 45456904350, 60609205800, 68719476736 ]
    
  • 2.2E6(2) 7 -block 73, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2.2E6(2).2 7 -block 102, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2.2E6(2).2 7 -block 103, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2) 7 -block 107, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2) 7 -block 141, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2) 7 -block 73, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2).2 7 -block 102, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2).2 7 -block 103, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2).2 7 -block 159, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2).3 7 -block 153, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2).3.2 7 -block 142, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2^2.2E6(2).3.2 7 -block 143, [ 19, 4199, 36465, 41990, 138567, 479655, 706401, 831402, 3464175, 6928350, 9183213, 10633194, 11884158, 16628040, 45916065, 59860944, 101015343, 101015343, 103194624, 118243840, 149652360, 254017536, 280598175, 295609600, 349668495, 505076715, 536870912 ]
    
  • 2.B 7 -block 4, [ 63532485, 356054375, 3214743741, 4221380670, 641238778125, 1095935366250, 1917448516791, 4836998684375, 7331420799495, 38658236225625, 78359378686875, 94981065075000, 162746401888125, 210919336847010, 652994822390625, 662947625486250, 665029816320000, 677025031854600, 718889622405120, 1198405322994375, 1370975689505565, 1711786747207680, 2123804897280000, 2565217512000000, 2642676197359616, 3469068040246875, 4231406449091250 ]
    
  • B 7 -block 4, [ 63532485, 356054375, 3214743741, 4221380670, 641238778125, 1095935366250, 1917448516791, 4836998684375, 7331420799495, 38658236225625, 78359378686875, 94981065075000, 162746401888125, 210919336847010, 652994822390625, 662947625486250, 665029816320000, 677025031854600, 718889622405120, 1198405322994375, 1370975689505565, 1711786747207680, 2123804897280000, 2565217512000000, 2642676197359616, 3469068040246875, 4231406449091250 ]
    
    

k(B) = 27, l(B) = 24

.. ..


• [ 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 7, 7, 7 ]

  • 7^2:(3x2S4) 7 -block 1, [ 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 48, 48, 48 ]
    
    

• [ ]

  
  
  • 2.F4(2).2 7 -block 1, [ 1, 1, 1326, 1326, 1377, 1377, 2210, 88400, 183600, 183600, 183600, 183600, 198900, 322218, 322218, 716040, 947700, 947700, 2685150, 5640192, 5640192, 5657600, 9052160, 16110900, 16777216, 16777216, 21481200 ]
    
  • F4(2).2 7 -block 1, [ 1, 1, 1326, 1326, 1377, 1377, 2210, 88400, 183600, 183600, 183600, 183600, 198900, 322218, 322218, 716040, 947700, 947700, 2685150, 5640192, 5640192, 5657600, 9052160, 16110900, 16777216, 16777216, 21481200 ]
    
  • Th 7 -block 1, [ 1, 248, 27000, 27000, 30628, 30875, 61256, 147250, 767637, 767637, 957125, 1707264, 1707264, 2450240, 4096000, 4096000, 4881384, 6669000, 6669000, 6696000, 6696000, 16539120, 51684750, 72925515, 76271625, 77376000, 190373976 ]
    
  • 2.B 7 -block 1, [ 1, 96255, 9550635, 4275362520, 9287037474, 156871952640, 6145833622500, 22348485900000, 47097393520320, 260522896303125, 386959894750000, 665029816320000, 775438738408125, 1679281227336960, 2991219686193960, 4068660047203125, 4331775591000000, 4331775591000000, 4643518737000000, 4919769220713750, 5223958579125000, 5992026614971875, 8774244412835616, 9211433539600384, 10134024677130240, 11381560819200000, 11854109736960000 ]
    
  • B 7 -block 1, [ 1, 96255, 9550635, 4275362520, 9287037474, 156871952640, 6145833622500, 22348485900000, 47097393520320, 260522896303125, 386959894750000, 665029816320000, 775438738408125, 1679281227336960, 2991219686193960, 4068660047203125, 4331775591000000, 4331775591000000, 4643518737000000, 4919769220713750, 5223958579125000, 5992026614971875, 8774244412835616, 9211433539600384, 10134024677130240, 11381560819200000, 11854109736960000 ]
    
  • 2.F4(2).2 7 -block 60, [ 13, 13, 5525, 5525, 11700, 11700, 27540, 141440, 141440, 212160, 286416, 358020, 795600, 2263040, 2263040, 2386800, 2386800, 2685150, 2864160, 3436992, 3790800, 3790800, 3790800, 3790800, 4194304, 4194304, 5728320 ]
    
  • 2.B 7 -block 73, [ 47, 5130, 200260, 4318548, 422138067, 2110690335, 4969652160, 10449529740, 11454872000, 11454872000, 15196970412, 29718731250, 67650331250, 82241557632, 82241557632, 765064872000, 1290369236992, 1290369236992, 1645948795392, 2058297312500, 2058297312500, 2075314305870, 4189738949253, 4189738949253, 4267940015625, 6154773016860, 11970536693760 ]
    
  • 2.B 7 -block 2, [ 4371, 1139374, 1407126890, 13508418144, 80426400000, 90807234375, 90807234375, 309720864375, 6697382793750, 8379477898506, 8379477898506, 17413195263750, 38348970335820, 140763279350304, 211069033500000, 422966584586250, 595404085985280, 835517991997440, 1042755084800000, 1370975689505565, 2611979289562500, 2788834713600000, 4231406449091250, 8351460096890625, 9211433539600384, 9558000449712000, 11854109736960000 ]
    
  • B 7 -block 2, [ 4371, 1139374, 1407126890, 13508418144, 80426400000, 90807234375, 90807234375, 309720864375, 6697382793750, 8379477898506, 8379477898506, 17413195263750, 38348970335820, 140763279350304, 211069033500000, 422966584586250, 595404085985280, 835517991997440, 1042755084800000, 1370975689505565, 2611979289562500, 2788834713600000, 4231406449091250, 8351460096890625, 9211433539600384, 9558000449712000, 11854109736960000 ]
    
  • M 7 -block 2, [ 52274355275, 435180535933, 988806680576, 1041414091734456, 54317097217968750, 64949219799742850, 323239147137500000, 9081069453503437500, 47568878129780509248, 108944448687780468750, 126355284567686718750, 287281642126153688442, 287281642126153688442, 666018487240132812500, 1031882028552810524232, 3921712560883625885696, 5269005456254138706250, 9423832305356325322752, 11454359687508997187500, 21376239229303664062500, 26791405009380518203125, 28773369016245329625666, 32246313392275328882250, 47965457043733625000000, 53966063314411884380160, 74121748343870517042012, 82550562284224841938560 ]
    
    

k(B) = 35, l(B) = 18

• (C7XC7):C2XC3XC37-block 1
  

• [ ]

  • 7:6xA7 7 -block 1, [ 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 36, 60, 60, 90 ]
    
    

k(B) = 35, l(B) = 27

.. ..


• [ 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5 ]

  • A17.2 7 -block 3, [ 8, 8, 272, 272, 2431, 2431, 6435, 10200, 10200, 58344, 58344, 79560, 79560, 116688, 116688, 121550, 121550, 176800, 176800, 291720, 291720, 291720, 291720, 350064, 350064, 454410, 454410, 486200, 486200, 525096, 525096, 631125, 663000, 663000, 729300 ]
    
    

• [ 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5 ]

  
  
  • A15.2 7 -block 1, [ 1, 1, 90, 90, 715, 715, 1430, 1430, 2925, 2925, 3432, 7722, 7722, 11583, 11583, 14300, 14300, 19305, 19305, 21450, 21450, 35100, 35100, 44550, 44550, 53625, 53625, 96525, 96525, 128700, 128700, 156000, 231660, 231660, 292864 ]
    
  • A16.2 7 -block 1, [ 1, 15, 104, 440, 1430, 2640, 3432, 3900, 6435, 14300, 16848, 24960, 36608, 42120, 45760, 51480, 68640, 71500, 82368, 85800, 91520, 105600, 114400, 115830, 171600, 231660, 266240, 292864, 337920, 411840, 416988, 429000, 429000, 549120, 673920 ]
    
  • A16.2 7 -block 2, [ 1, 15, 104, 440, 1430, 2640, 3432, 3900, 6435, 14300, 16848, 24960, 36608, 42120, 45760, 51480, 68640, 71500, 82368, 85800, 91520, 105600, 114400, 115830, 171600, 231660, 266240, 292864, 337920, 411840, 416988, 429000, 429000, 549120, 673920 ]
    
  • A17.2 7 -block 1, [ 1, 120, 1105, 1700, 3536, 7072, 11440, 15912, 19448, 37400, 48620, 65637, 70720, 87516, 116688, 121550, 134640, 145860, 155584, 194480, 291720, 318240, 364650, 388960, 466752, 486200, 848640, 972400, 1454112, 1591200, 1750320, 1750320, 2362932, 2431000, 3620864 ]
    
  • A17.2 7 -block 2, [ 1, 120, 1105, 1700, 3536, 7072, 11440, 15912, 19448, 37400, 48620, 65637, 70720, 87516, 116688, 121550, 134640, 145860, 155584, 194480, 291720, 318240, 364650, 388960, 466752, 486200, 848640, 972400, 1454112, 1591200, 1750320, 1750320, 2362932, 2431000, 3620864 ]
    
    

• [ 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]

  
  
  • A14.2 7 -block 1, [ 1, 1, 13, 13, 78, 78, 286, 286, 429, 429, 715, 715, 1287, 1287, 1716, 1716, 4576, 4576, 6435, 6435, 9504, 15444, 15444, 21450, 21450, 21450, 21450, 24960, 24960, 36608, 36608, 59904, 68640, 69498, 69498 ]
    
    

• [ ]

  
  
  • O12+(2).2 7 -block 1, [ 1, 1, 1364, 1364, 92752, 371008, 371008, 417384, 417384, 1988712, 1988712, 7588800, 7588800, 8724672, 8724672, 21130065, 21130065, 23744512, 23744512, 26712576, 26712576, 37100800, 127277568, 127277568, 211300650, 357564416, 357564416, 379912192, 422601300, 422601300, 1073741824, 1073741824, 1352324160, 1352324160, 1690405200 ]
    
  • A16 7 -block 1, [ 1, 15, 104, 440, 1430, 2640, 3432, 3900, 6435, 14300, 16848, 24960, 36608, 42120, 45760, 51480, 68640, 71500, 82368, 85800, 91520, 105600, 114400, 115830, 171600, 231660, 266240, 292864, 337920, 411840, 416988, 429000, 429000, 549120, 673920 ]
    
  • A17 7 -block 1, [ 1, 120, 1105, 1700, 3536, 7072, 11440, 15912, 19448, 37400, 48620, 65637, 70720, 87516, 116688, 121550, 134640, 145860, 155584, 194480, 291720, 318240, 364650, 388960, 466752, 486200, 848640, 972400, 1454112, 1591200, 1750320, 1750320, 2362932, 2431000, 3620864 ]
    
    

k(B) = 49, l(B) = 48

.. ..


• [ ]

  • 2.L2(49).2_1 7 -block 1, [ 1, 1, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50 ]
    
  • L2(49).2_1 7 -block 1, [ 1, 1, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50 ]
    
  • 2.L2(49).2_1 7 -block 4, [ 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25 ]
    

References:

[Hol], M. Holloway, Derived\ Equivalences for group algebras, thesis, Univ. of Bristol, (2001).

[HS], M. Hasan Ali and M. Schaps, Lifting McKay graphs \ and relations, Rocky Moun.J.

[KosKun1], S. Koshitani and N. Kunugi, The princip\ al 3-blocks of the 3-dimensional projective special unitary groups in non-defining characteristic, (1997).

[MS], J. Mueller and M. Schaps, The Broue conjecture for the faithful blocks of 4.M22, preprint.

[O], T. Okuyama, Some examples of derived equivalent blocks of finite groups, preprint.

Last Update: June 3, 2006,using IndexOfBlocks.gap, created by M.Schaps and GAP4, version 4.2; Aachen, St Andrews, 1999, http://www-gap.dcs.st-and.ac.\ u,/~gap