Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#13405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C2×#41×C131 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C22×C4×C131 ◁ C2×#131×C131 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 195 |
| transitive degree | μt(G) = 8384 |
A minimal faithful permutation representation — 3 generators on 195 points:
(1,2,7,12)(3,13,18,34)(4,19,23,56)(5,24,27,10)(6,28,31,55)(8,17,35,15)(9,36,39,22)(11,41,44,26)(14,47,20,57)(16,33,29,42)(21,59,25,43)(30,40,60,38)(32,61,37,52)(45,58,62,49)(46,51,63,53)(48,64,50,54)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195);(1,3)(2,8)(4,20)(5,17)(6,29)(7,18)(9,37)(10,34)(11,42)(12,35)(13,24)(14,23)(15,27)(16,31)(19,54)(21,48)(22,49)(25,50)(26,51)(28,46)(30,52)(32,39)(33,44)(36,58)(38,62)(40,45)(41,53)(43,47)(55,63)(56,64)(57,59)(60,61);(1,4,7,23)(2,9,12,39)(3,14)(5,25,27,21)(6,30,31,60)(8,32)(10,40,24,38)(11,43,44,59)(13,45)(15,50)(16,52)(17,48)(18,20)(19,55,56,28)(22,41,36,26)(29,61)(33,47)(34,62)(35,37)(42,57)(46,64)(49,53)(51,58)(54,63)4454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 6393);