Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#18039 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C2×C13×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20,18,16,19,21)(22,23,27,30)(24,31,33,36)(25,29,26,34)(28,35,37,32);(22,24,27,33)(23,28,30,37)(25,32,26,35)(29,36,34,31);(14,16,17,21,18,15,19,20);(15,16)(20,21)(22,25,27,26)(23,29,30,34)(24,32,33,35)(28,36,37,31)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11027);