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×#13260 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #459 |
| 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 ◁ C2×C4×C8×C13 ◁ G | |
482 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)(18,19,22,27,40,28,38,44,24,30,37,26,23,29,21,36)(20,31,32,46,33,41,48,43,35,47,49,42,34,45,39,25);(14,15,16,17)(18,20)(19,25)(21,32)(22,39)(23,33)(24,35)(26,41)(27,45)(28,42)(29,46)(30,43)(31,36)(34,40)(37,48)(38,49)(44,47);(18,21,23,37,24,38,40,22)(19,26,28,36,30,27,29,44)(20,32,33,48,35,49,34,39)(25,41,42,31,43,45,46,47)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6248);