Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33463 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | C2×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C2×C13 | C2×C4×D8 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24,20,23,35,25)(16,26,28,37,30,43,29,45)(17,22,31,41,32,40,18,33)(21,36,39,44,38,34,42,27);(14,16)(15,21)(17,27)(18,34)(19,28)(20,30)(22,37)(23,38)(24,39)(25,42)(26,33)(29,35)(31,36)(32,44)(40,45)(41,43);(14,17,19,31,20,32,35,18)(15,22,24,41,23,40,25,33)(16,27,28,36,30,44,29,34)(21,37,39,43,38,45,42,26);(15,23)(21,38)(22,40)(24,25)(26,43)(33,41)(37,45)(39,42)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26451);