Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33617 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×#466 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ 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)(16,28)(17,35)(18,24)(19,41)(20,26)(21,27)(22,32)(23,38)(25,29)(30,58)(31,53)(33,54)(34,55)(36,48)(37,68)(39,51)(40,50)(42,49)(43,70)(44,63)(45,56)(46,64)(47,69)(52,61)(57,66)(59,74)(60,65)(62,75)(67,73)(71,76)(72,77);(14,16,29,56,20,33,42,64,21,34,40,63,18,31,19,32)(15,22,41,53,24,44,50,55,27,46,49,54,26,45,25,28)(17,30,57,70,38,61,69,77,39,62,67,76,36,59,37,60)(23,43,66,58,35,65,68,74,48,71,73,75,51,72,47,52);(14,17)(15,23)(16,30)(18,36)(19,37)(20,38)(21,39)(22,43)(24,35)(25,47)(26,51)(27,48)(28,52)(29,57)(31,59)(32,60)(33,61)(34,62)(40,67)(41,66)(42,69)(44,65)(45,72)(46,71)(49,73)(50,68)(53,58)(54,75)(55,74)(56,70)(63,76)(64,77);(14,18,21,20)(15,24,27,26)(16,31,34,33)(17,36,39,38)(19,40,42,29)(22,44,46,45)(23,35,48,51)(25,41,50,49)(28,53,55,54)(30,59,62,61)(32,63,64,56)(37,67,69,57)(43,65,71,72)(47,66,68,73)(52,58,74,75)(60,76,77,70)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26605);