Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
480 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)(15,17)(18,19,24,31,27,36,23,35,26,32,22,29,25,20,33,30)(21,37,40,28,44,46,39,34,42,49,38,48,41,45,43,47);(14,15,16,17)(18,20,26,36)(19,27,32,25)(21,34,42,47)(22,31,24,29)(23,35,33,30)(28,41,48,44)(37,43,49,39)(38,45,40,46);(18,21,26,42)(19,28,32,48)(20,34,36,47)(22,39,24,43)(23,38,33,40)(25,44,27,41)(29,49,31,37)(30,46,35,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6006);