Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C25 |
| direct product | C131×#22892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | D42 |
| commutator | C2×C4 | C23×C4×C131 |
| Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C2×2−1+4×C131 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 8384 |
A minimal faithful permutation representation — 4 generators on 167 points:
(1,2,4,3)(5,6,12,18)(7,19,8,22)(9,15,27,33)(10,17,11,16)(13,24,14,21)(20,35,23,31)(25,30,36,29)(26,34,28,32)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167);(1,3,4,2)(5,7,12,8)(6,13,18,14)(9,25,27,36)(10,24,11,21)(15,31,33,35)(16,22,17,19)(20,28,23,26)(29,34,30,32);(5,8,12,7)(6,14,18,13)(9,23,27,20)(10,24,11,21)(15,30,33,29)(16,22,17,19)(25,26,36,28)(31,32,35,34);(5,9)(6,15)(7,20)(8,23)(10,28)(11,26)(12,27)(13,29)(14,30)(16,34)(17,32)(18,33)(19,35)(21,36)(22,31)(24,25)6812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 15880);