Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33596 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
674 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)(14,15,21,27)(16,28,30,47)(17,34,37,67)(18,26,20,24)(19,39,42,51)(22,33,45,31)(23,48,50,36)(25,38,53,41)(29,57,58,77)(32,46,61,73)(35,68,43,52)(40,54,70,49)(44,71,72,63)(55,75,74,60)(56,62,69,64)(59,66,65,76);(14,16,18,31,21,30,20,33)(15,22,24,28,27,45,26,47)(17,29,35,59,37,58,43,65)(19,32,38,62,42,61,41,64)(23,44,49,55,50,72,54,74)(25,46,51,56,53,73,39,69)(34,66,52,57,67,76,68,77)(36,60,40,63,48,75,70,71);(14,17)(15,23)(16,29)(18,35)(19,40)(20,43)(21,37)(22,44)(24,49)(25,52)(26,54)(27,50)(28,55)(30,58)(31,59)(32,63)(33,65)(34,39)(36,41)(38,48)(42,70)(45,72)(46,57)(47,74)(51,67)(53,68)(56,76)(60,64)(61,71)(62,75)(66,69)(73,77);(16,30)(22,45)(28,47)(29,58)(31,33)(32,61)(44,72)(46,73)(55,74)(56,69)(57,77)(59,65)(60,75)(62,64)(63,71)(66,76)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26584);