Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10867 |
| 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×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C13×M16 ◁ G | |
714 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)(18,19,23,28,24,27,22,37)(20,29,31,40,32,25,38,41)(21,33,35,42,36,48,34,26)(30,44,45,43,46,47,49,39);(14,15,16,17)(18,20)(19,25)(21,30)(22,31)(23,38)(24,32)(26,39)(27,29)(28,40)(33,47)(34,45)(35,49)(36,46)(37,41)(42,43)(44,48);(18,21,22,34,24,36,23,35)(19,26,28,33,27,42,37,48)(20,30,31,45,32,46,38,49)(25,39,40,47,29,43,41,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3855);