Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13033 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13033 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1879 |
| 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 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
498 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)(14,15,18,23,19,24,33,41,20,25,17,31,34,43,35,22)(16,26,28,39,29,42,36,40,30,38,27,44,37,45,32,21);(14,16)(15,21,25,40)(17,32)(18,36)(19,37)(20,30)(22,38,41,26)(23,42,31,45)(24,44,43,39)(27,35)(28,33)(29,34);(15,22)(17,33)(18,35)(19,34)(21,38)(23,43)(24,31)(25,41)(26,40)(27,36)(28,32)(29,37)(39,42)(44,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6021);