Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13030 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1879 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
476 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)(14,15,18,23,19,25,35,39,20,26,17,24,34,43,32,21)(16,27,29,40,30,42,36,41,31,38,28,45,37,44,33,22);(15,21,26,39)(17,32)(18,35)(19,34)(22,38,41,27)(23,25,24,43)(28,33)(29,36)(30,37)(40,42,45,44);(14,16)(15,22)(17,33)(18,36)(19,37)(20,31)(21,38)(23,42)(24,44)(25,45)(26,41)(27,39)(28,32)(29,35)(30,34)(40,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6018);