Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
494 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)(18,19,21,27,38,42,22,28,24,30,39,43,23,29,36,25)(20,31,32,26,40,44,37,48,35,47,49,46,34,41,33,45);(14,15,16,17)(19,25)(21,36)(22,39)(23,38)(26,41)(27,29)(28,30)(31,45)(32,33)(34,40)(37,49)(42,43)(44,46)(47,48);(18,20)(19,26)(21,37)(22,32)(23,40)(24,35)(25,41)(27,47)(28,44)(29,48)(30,46)(31,43)(33,39)(34,38)(36,49)(42,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6010);