Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #459 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
476 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)(14,15)(16,17)(18,19,24,31,44,45,43,29,26,33,23,30,25,32,22,42)(20,34,37,27,41,28,35,48,39,49,36,47,38,46,21,40);(18,20,25,41,26,39,44,38)(19,27,45,40,33,47,32,48)(21,22,37,23,35,43,36,24)(28,31,34,29,46,30,49,42);(15,17)(18,21)(19,28)(20,22)(23,41)(24,38)(25,37)(26,35)(27,31)(29,40)(30,47)(32,49)(33,46)(34,45)(36,44)(39,43)(42,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6016);