Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C24 |
| direct product | C131×#29902 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #2622 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | #3008×C131 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C22×C4×C131 ◁ G | |
772 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)(3,8)(4,10)(5,11)(6,9)(7,12)(13,23)(14,21)(15,22)(16,20)(17,26)(18,24)(19,25)(27,32)(28,30)(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);(1,3,6,13,5,16,7,15)(2,8,12,22,11,20,9,23)(4,14,18,27,17,28,19,29)(10,21,25,31,26,30,24,32);(2,9)(3,13)(4,17)(6,7)(8,20)(10,25)(11,12)(14,27)(15,16)(21,30)(24,26)(28,29);(1,4)(2,10)(3,14)(5,17)(6,18)(7,19)(8,21)(9,24)(11,26)(12,25)(13,27)(15,29)(16,28)(20,30)(22,31)(23,32)4454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 22890);