Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13246 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| 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 | |
422 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)(18,19,24,30,25,32,44,31)(20,33,37,46,39,21,38,41)(22,42,23,28,34,29,45,49)(26,27,47,35,48,36,40,43);(14,15,16,17)(18,20,34,35,24,38,45,27,25,39,22,43,44,37,23,36)(19,26,28,21,31,47,42,41,32,48,49,33,30,40,29,46);(18,21,22,40,24,41,23,26,25,33,34,47,44,46,45,48)(19,27,49,20,31,43,29,38,32,36,28,39,30,35,42,37)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6234);