Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C25×C4 |
| direct product | C131×#33358 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C131 | C2×#99 |
| commutator | C2×C4 | C23×C4×C131 |
| Frattini, cosocle | C2×D4 | C24×C131 |
| socle | C2×C131 | C22×#99 |
| prime radical | #3449×C131 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C131 ◁ C22×C4×C131 ◁ C22×#41×C131 ◁ G | |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 4192 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2)(3,11,12,24)(4,8)(5,17,19,9)(6,10)(7,14)(13,25,26,32)(15,28,30,22)(16,23)(18,20)(21,27)(29,31)(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)(2,7)(4,13)(5,18)(6,12)(8,21)(9,24)(10,20)(11,17)(14,19)(15,29)(16,26)(22,32)(23,31)(25,28)(27,30);(3,12)(7,20)(11,24)(13,26)(14,18)(21,31)(25,32)(27,29);(1,4,6,16)(2,8,10,23)(3,13,12,26)(5,15,19,30)(7,21,20,31)(9,22,17,28)(11,25,24,32)(14,27,18,29)6026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26346);