Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#11685 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #327 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C2×M16 | C23×C13 |
| socle | C2×C13 | C2×#327 |
| prime radical | C13×#3054 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
448 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)(16,25,28,42)(17,22)(18,31,33,45)(19,35)(20,24)(21,27)(23,30,40,34)(26,41,29,39)(32,36)(37,43)(38,44);(14,16)(15,21)(17,26)(18,32)(19,29)(20,28)(22,36)(23,39)(24,38)(25,31)(27,34)(30,44)(33,43)(35,37)(40,41)(42,45);(14,17,20,19)(15,22,24,35)(16,26,28,29)(18,30,33,34)(21,36,38,37)(23,31,40,45)(25,41,42,39)(27,32,44,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4673);