Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C25 |
| direct product | C131×#25198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C131 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | #3020×C131 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C22×C4×C131 ◁ G | |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 4192 |
A minimal faithful permutation representation — 4 generators on 163 points:
(1,2,5,10,6,11,21,9)(3,12,15,23,16,25,14,7)(4,17,19,24,20,26,18,8)(13,22,28,31,29,32,30,27)(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);(1,3,5,15,6,16,21,14)(2,7,10,12,11,23,9,25)(4,13,19,28,20,29,18,30)(8,22,17,31,24,32,26,27);(1,4,6,20)(2,8,11,24)(3,13,16,29)(5,18,21,19)(7,22,23,32)(9,17,10,26)(12,27,25,31)(14,28,15,30);(1,2)(3,7)(4,8)(5,10)(6,11)(9,21)(12,15)(13,22)(14,25)(16,23)(17,19)(18,26)(20,24)(27,30)(28,31)(29,32)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 18186);