Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C23×C4 |
| direct product | C131×#29724 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C24×C131 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G | |
922 conjugacy classes of subgroups.
| minimal degree | μ(G) = 175 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 175 points:
(1,2,3,4)(5,6)(7,10)(8,9)(11,12)(13,14)(15,19)(16,20)(17,22)(18,21)(23,32)(24,34)(25,33)(26,35)(27,37)(28,36)(29,39)(30,40)(31,38)(41,43)(42,44)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175);(6,9)(10,12)(13,15,18,25)(14,19,21,33)(16,26,28,42)(17,29,31,24)(20,35,36,44)(22,39,38,34)(23,30,41,27)(32,40,43,37);(2,4)(5,7)(6,10)(8,11)(9,12)(13,16,18,28)(14,20,21,36)(15,23,25,41)(17,30,31,27)(19,32,33,43)(22,40,38,37)(24,42,29,26)(34,44,39,35);(7,11)(10,12)(14,21)(19,33)(20,36)(22,38)(32,43)(34,39)(35,44)(37,40)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 22712);