Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#13414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C22×D8×C131 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×C4×C8×C131 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 8384 |
A minimal faithful permutation representation — 3 generators on 167 points:
(1,2)(3,4)(5,6,11,16)(7,17,20,35)(8,12,10,14)(9,22,25,32)(13,28,31,18)(15,21,33,23)(19,29,26,34)(24,30,36,27)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167);(6,12)(7,18)(8,10)(9,23)(13,29)(14,16)(15,33)(17,27)(19,24)(20,28)(21,25)(26,36)(30,35)(31,34);(2,4)(5,7,8,19,11,20,10,26)(6,13,14,30,16,31,12,27)(9,24,21,18,25,36,23,28)(15,29,32,17,33,34,22,35)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 6402);