Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33442 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | C22×D4 |
| commutator | C4 | C23×C8×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×C8×D4 |
| prime radical | C13×#575 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C2×C13×M32 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,25,20,24,39,49,21,26,40,50,18,36,38,62)(16,27,30,52,29,22,41,43,31,44,56,68,37,45,63,69)(17,23,34,48,35,47,61,71,32,46,57,70,33,58,60,74)(28,51,55,72,54,42,64,66,53,67,73,77,59,65,75,76);(14,16)(15,22)(17,28)(18,37)(19,30)(20,29)(21,31)(23,42)(24,44)(25,43)(26,45)(27,36)(32,53)(33,59)(34,55)(35,54)(38,63)(39,41)(40,56)(46,65)(47,67)(48,66)(49,68)(50,69)(51,58)(52,62)(57,73)(60,75)(61,64)(70,76)(71,77)(72,74);(14,17,19,34,20,35,39,61,21,32,40,57,18,33,38,60)(15,23,25,48,24,47,49,71,26,46,50,70,36,58,62,74)(16,28,30,55,29,54,41,64,31,53,56,73,37,59,63,75)(22,42,43,66,44,67,68,77,45,65,69,76,27,51,52,72);(17,32)(23,46)(28,53)(33,35)(34,57)(42,65)(47,58)(48,70)(51,67)(54,59)(55,73)(60,61)(64,75)(66,76)(71,74)(72,77)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26430);