Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11669 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12829 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #418 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1804 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
378 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26,29,21)(17,31)(18,35)(19,41)(20,23)(22,33)(24,39)(25,38)(27,54,55,73)(28,58,36,69)(30,45,61,53)(32,64)(34,67)(37,51)(40,68)(42,50)(43,56,52,66)(44,62,49,71)(46,72)(47,65)(48,59)(57,75,63,77)(60,74,70,76);(14,16,19,30,20,29,38,61)(15,21,41,53,23,26,25,45)(17,27,42,63,32,55,34,57)(18,36,39,71,40,28,59,62)(22,43,46,74,47,52,51,76)(24,49,68,69,48,44,35,58)(31,54,50,77,64,73,67,75)(33,66,72,60,65,56,37,70);(14,17)(15,22)(16,27)(18,37)(19,42)(20,32)(21,43)(23,47)(24,50)(25,51)(26,52)(28,60)(29,55)(30,63)(31,35)(33,39)(34,38)(36,70)(40,72)(41,46)(44,75)(45,76)(48,67)(49,77)(53,74)(54,58)(56,62)(57,61)(59,65)(64,68)(66,71)(69,73)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5817);