Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#8241 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | C4×C22⋊C4 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
452 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)(15,18)(16,20)(22,23,26,30,27,31,25,28)(24,29,33,36,34,37,32,35);(14,15,16,19,17,18,20,21)(23,28,31,30)(29,35,37,36);(22,24,26,33,27,34,25,32)(23,29,30,36,31,37,28,35)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1229);