Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#12043 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×D8 |
| commutator | C8 | C22×C8×C13 |
| Frattini, cosocle | C4×C8 | C23×C13 |
| socle | C22×C13 | C4×D8 |
| prime radical | C2×C13×D8 | C2×C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C4×C8×C13 ◁ C82×C13 ◁ G | |
238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 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)(24,27)(25,34)(26,28)(29,31)(30,32)(33,35)(36,37);(23,27)(24,31)(25,32)(28,35)(29,30)(33,37)(34,36);(14,16,17,21,18,15,19,20)(23,28)(27,35)(29,36)(30,34)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5031);