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×#10868 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #382 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
730 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)(14,15)(16,17)(18,19)(20,29,32,25)(21,34)(22,38)(23,28)(24,27)(26,35)(30,44,46,48)(31,40,33,43)(36,41)(37,49)(39,45,42,47);(15,17)(18,20,23,33,24,32,22,31)(19,25,28,40,27,29,38,43)(21,30,36,47,37,46,35,45)(26,39,34,48,41,42,49,44);(18,21,22,35,24,37,23,36)(19,26,28,34,27,41,38,49)(20,30,31,45,32,46,33,47)(25,39,40,48,29,42,43,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3856);