Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12596 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
310 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)(18,19,23,28,22,30,38,45,24,29,40,26,39,27,21,36)(20,31,34,46,33,25,32,41,35,43,47,49,48,42,37,44);(14,15,16,17)(18,20)(19,25,29,42)(21,37)(22,33)(23,34)(24,35)(26,44,28,41)(27,31,30,43)(32,38)(36,46,45,49)(39,48)(40,47);(18,21,22,23,24,38,39,40)(19,26,27,45,29,28,30,36)(20,32,33,47,35,37,48,34)(25,41,31,46,42,44,43,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5584);