Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13230 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1964 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
436 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)(16,26,31,49)(17,32)(18,37,27,23)(19,40)(20,25)(21,29)(22,35)(24,33)(28,52,56,75)(30,58,53,48)(34,63,50,60)(36,61)(38,43)(39,46,51,67)(41,70)(42,68)(44,65,66,74)(45,62)(47,72,73,55)(54,59)(57,69)(64,76)(71,77);(14,16,27,29,20,31,18,38)(15,21,37,49,25,43,23,26)(17,28,50,54,36,56,34,64)(19,30,51,57,33,53,39,68)(22,41,66,73,45,71,44,47)(24,42,67,58,40,69,46,48)(32,59,63,75,61,76,60,52)(35,55,74,70,62,72,65,77);(14,17,33,62,20,36,19,35)(15,22,40,61,25,45,24,32)(16,28,53,72,31,56,30,55)(18,34,51,74,27,50,39,65)(21,41,69,76,43,71,42,59)(23,44,67,63,37,66,46,60)(26,47,58,75,49,73,48,52)(29,54,68,77,38,64,57,70)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6218);