Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C131 · Schur multiplier (H2) = C25 |
| direct product | C131×#33410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | C22×D8 |
| commutator | C8 | C23×C4×C131 |
| Frattini, cosocle | C2×C8 | C24×C131 |
| prime radical | C2×#41×C131 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×#41×C131 ◁ C2×#131×C131 ◁ G | |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 167 |
| transitive degree | μt(G) = 16768 |
A minimal faithful permutation representation — 4 generators on 167 points:
(1,2,3,4)(6,11)(8,12)(9,19)(13,21)(14,29)(15,24)(17,25)(18,31)(20,26)(22,23)(27,32)(28,36)(30,35)(33,34)(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);(5,6,12,23,9,14,20,24,10,15,26,29,19,22,8,11)(7,13,25,34,18,28,30,32,16,27,35,36,31,33,17,21);(5,7)(6,13)(8,17)(9,18)(10,16)(11,21)(12,25)(14,28)(15,27)(19,31)(20,30)(22,33)(23,34)(24,32)(26,35)(29,36);(7,16)(13,27)(17,30)(18,31)(21,32)(25,35)(28,33)(34,36)8384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 26398);