Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2023 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24,26,41)(17,29)(18,33)(19,22)(20,27,25,43)(21,31)(23,35)(28,37,34,42)(30,39,45,36)(32,40)(38,44);(14,15)(16,25,26,20)(17,21)(18,23)(19,22)(24,27,41,43)(28,39,34,36)(29,31)(30,42,45,37)(32,38)(33,35)(40,44);(14,16)(15,20)(17,30)(18,34)(19,26)(21,37)(22,25)(23,39)(24,40)(27,44)(28,35)(29,41)(31,43)(32,45)(33,36)(38,42)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6362);