Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13019 |
| 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 | |
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)(18,19,23,27,39,48,22,40,25,31,21,28,24,30,41,29)(20,32,35,46,42,43,38,26,37,45,33,49,36,44,34,47);(14,15,16,17)(18,20)(19,26)(21,38)(22,33)(23,34)(24,42)(25,37)(27,43)(28,44)(29,45)(30,49)(31,47)(32,40)(35,41)(36,39)(46,48);(19,27)(21,22)(23,41)(24,39)(26,43)(28,31)(29,48)(30,40)(32,49)(33,38)(34,35)(36,42)(44,47)(45,46)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6007);