Finite Group DatabasebetaFinite Group Databasebeta| order | 33536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C131 · Schur multiplier (H2) = C26 |
| direct product | C131×#23464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| prime radical | C24×C131 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G | |
1146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 8384 |
A minimal faithful permutation representation — 4 generators on 171 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,23)(13,18)(14,27)(15,19)(17,25)(20,36)(21,30)(22,32)(24,34)(26,35)(28,31)(29,37)(33,39)(38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(1,3,4,8)(2,5,6,7)(9,11)(10,16)(12,20)(13,21)(14,28)(15,22)(17,33)(18,30)(19,32)(23,36)(24,37)(25,39)(26,38)(27,31)(29,34)(35,40);(9,12,15,26)(10,17,19,34)(11,20,22,38)(13,25,14,24)(16,29,32,33)(18,35,27,23)(21,39,28,37)(30,36,31,40);(9,13,15,14)(10,18,19,27)(11,21,22,28)(12,24,26,25)(16,30,32,31)(17,23,34,35)(20,37,38,39)(29,40,33,36)6026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33536, 16452);