Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#8909 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #385 |
| prime radical | C23×C13 | C22⋊Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
376 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)(15,19)(16,20)(17,21)(22,23,26,30,27,31,25,29)(24,32,34,28,35,36,33,37);(14,15,18,16)(17,20,21,19)(22,24,25,33,27,35,26,34)(23,28,29,32,31,37,30,36);(14,16,18,15)(17,19,21,20)(22,25,27,26)(23,29,31,30)(24,33,35,34)(28,32,37,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1897);