Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33465 |
| 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 | C2×C13×#508 | 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)(14,15,19,26,21,24,20,41)(16,27,30,54,31,53,42,51)(17,23,34,48,32,49,35,64)(18,36,38,50,40,66,39,25)(22,37,45,58,44,67,46,29)(28,52,57,73,55,74,65,71)(33,60,62,72,59,76,63,47)(43,61,68,75,70,77,69,56);(14,16)(15,22)(17,28)(18,37)(19,30)(20,42)(21,31)(23,43)(24,44)(25,51)(26,45)(27,36)(29,39)(32,55)(33,61)(34,57)(35,65)(38,58)(40,67)(41,46)(47,71)(48,68)(49,70)(50,54)(52,60)(53,66)(56,63)(59,77)(62,75)(64,69)(72,73)(74,76);(14,17,19,34,21,32,20,35)(15,23,26,48,24,49,41,64)(16,28,30,57,31,55,42,65)(18,33,38,62,40,59,39,63)(22,43,45,68,44,70,46,69)(25,47,36,60,50,72,66,76)(27,52,54,73,53,74,51,71)(29,56,37,61,58,75,67,77);(15,24)(17,32)(22,44)(25,50)(26,41)(27,53)(28,55)(33,59)(34,35)(36,66)(45,46)(51,54)(56,75)(57,65)(61,77)(62,63)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26453);