Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#23382 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C131 | C24 |
| commutator | C23 | C23×C4×C131 |
| Frattini, cosocle | C22×C4 | C24×C131 |
| socle | C23×C131 | C23×C4 |
| prime radical | C24×C131 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C131 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2)(3,7)(4,5)(6,8)(9,10,12,14)(11,13,16,15)(17,18,21,24,20,22,27,29)(19,23,26,30,25,28,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(1,2)(3,6)(4,5)(7,8)(9,10)(11,15)(12,14)(13,16)(18,22)(23,28)(24,29)(30,32);(2,5)(6,7)(9,11,12,16)(10,13,14,15)(17,19,20,25)(18,23,22,28)(21,26,27,31)(24,30,29,32);(1,3,4,8)(2,6,5,7)(10,14)(13,15)(18,22)(19,25)(24,29)(26,31)6812 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 16370);