Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C22×C4 |
| direct product | C131×#29119 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C22×#41×C131 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G | |
842 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)(4,6)(5,8)(9,10,12,14)(11,13,15,16)(17,18,21,26,22,27,20,25)(19,23,28,31,29,32,30,24)(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);(1,3,4,8)(2,5,6,7)(9,11,12,15)(10,13,14,16)(17,19)(18,23)(20,30)(21,28)(22,29)(24,25)(26,31)(27,32);(11,15)(13,16)(17,19)(18,24)(20,28)(21,30)(22,29)(23,25)(26,32)(27,31);(2,6)(5,7)(17,20,22,21)(18,25,27,26)(19,28,29,30)(23,31,32,24)6026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 22107);