Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C25 |
| direct product | C131×#33604 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C131 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C131 |
| socle | C22×C131 | C22×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C131 ◁ C23×C4×C131 ◁ C23×C8×C131 ◁ G | |
690 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)(3,4)(5,6)(7,16)(8,13)(9,23)(10,25)(11,15)(12,20)(14,17)(18,29)(19,30)(21,35)(22,28)(24,36)(26,33)(27,34)(31,32)(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);(5,7,17,32,10,21,24,33,11,18,22,34,8,19,9,20)(6,12,23,30,13,27,28,29,15,26,36,35,25,31,14,16);(2,4)(7,18)(12,26)(16,29)(19,21)(20,33)(27,31)(30,35)(32,34);(5,8,11,10)(6,13,15,25)(7,19,18,21)(9,22,24,17)(12,27,26,31)(14,23,28,36)(16,30,29,35)(20,34,33,32)6812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26592);