Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #481 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C24×C13 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
496 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)(18,19,22,28,39,41,36,27,24,26,37,45,23,29,21,35)(20,30,33,25,40,43,31,47,32,48,49,42,34,46,38,44);(14,15,16,17)(18,20,23,40,24,32,39,34)(19,25,41,44,26,42,29,47)(21,33,37,31,36,49,22,38)(27,46,45,48,35,43,28,30);(19,26)(21,36)(22,37)(25,42)(29,41)(31,38)(33,49)(44,47)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5997);