Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33464 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×C4×D8 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C13×M16 ◁ C13×#405 ◁ 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)(14,15,19,25,21,26,20,41)(16,27,30,53,31,54,42,50)(17,23,34,49,32,47,35,64)(18,36,38,51,40,66,39,24)(22,37,44,58,46,67,45,29)(28,52,57,74,55,73,65,72)(33,60,62,71,59,76,63,48)(43,61,69,75,68,77,70,56);(14,16)(15,22)(17,28)(18,37)(19,30)(20,42)(21,31)(23,43)(24,50)(25,44)(26,46)(27,36)(29,39)(32,55)(33,61)(34,57)(35,65)(38,58)(40,67)(41,45)(47,68)(48,72)(49,69)(51,53)(52,60)(54,66)(56,63)(59,77)(62,75)(64,70)(71,74)(73,76);(14,17,19,34,21,32,20,35)(15,23,25,49,26,47,41,64)(16,28,30,57,31,55,42,65)(18,33,38,62,40,59,39,63)(22,43,44,69,46,68,45,70)(24,48,36,60,51,71,66,76)(27,52,53,74,54,73,50,72)(29,56,37,61,58,75,67,77);(17,32)(23,47)(28,55)(33,59)(34,35)(43,68)(48,71)(49,64)(52,73)(56,75)(57,65)(60,76)(61,77)(62,63)(69,70)(72,74)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26452);