Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C131 · Schur multiplier (H2) = C23 |
| direct product | C131×#13412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C2×#135×C131 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ #405×C131 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 3 generators on 167 points:
(2,3)(5,6)(7,12)(8,13)(9,26)(10,27)(11,16)(14,23)(15,24)(17,35)(18,31)(19,36)(20,29)(21,33)(22,30)(25,34)(28,32)(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);(1,2)(3,4)(5,7,11,21)(6,12,16,33)(8,22,25,19)(9,17,23,18)(10,28,24,20)(13,30,34,36)(14,31,26,35)(15,29,27,32);(1,3,4,2)(6,13)(7,17)(8,23)(9,25)(10,24)(12,29)(14,15)(16,34)(18,21)(19,28)(20,22)(26,27)(31,35)(32,33)5240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 6400);