Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13034 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1879 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
462 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)(14,15,19,24,20,26,45,57,21,27,18,25,41,56,42,60)(16,28,31,49,32,54,43,50,33,64,30,61,46,58,39,22)(17,34,36,62,37,55,40,23,38,51,35,52,47,59,44,53)(29,48,66,72,67,73,69,76,68,74,65,77,71,75,70,63);(14,16)(15,22,27,50)(17,29)(18,39)(19,43)(20,46)(21,33)(23,48,53,74)(24,54,25,58)(26,61,56,49)(28,60,64,57)(30,42)(31,45)(32,41)(34,63,51,76)(35,70)(36,69)(37,71)(38,68)(40,66)(44,65)(47,67)(52,75,62,73)(55,77,59,72);(14,17,21,38)(15,23,27,53)(16,29,33,68)(18,40,19,44)(20,47,41,37)(22,48,50,74)(24,55,25,59)(26,62,56,52)(28,63,64,76)(30,69,31,70)(32,71,46,67)(34,60,51,57)(35,42,36,45)(39,66,43,65)(49,75,61,73)(54,77,58,72)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6022);