Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C22×C42 |
| direct product | C13×#10814 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #380 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C13×M16 ◁ G | |
658 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,30)(21,35,37,42)(22,28)(23,27)(24,29)(25,32)(26,36,43,38)(31,39,46,49)(33,41)(34,40)(44,45,48,47);(14,15,16,17)(18,20,23,33,24,34,22,32)(19,25,28,40,29,41,27,30)(21,31,38,47,37,46,36,45)(26,39,35,48,43,49,42,44);(18,21,22,36,24,37,23,38)(19,26,27,42,29,43,28,35)(20,31,32,45,34,46,33,47)(25,39,30,44,41,49,40,48)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3802);