Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9860 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #127 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #390 |
| prime radical | C13×#3147 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
498 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)(16,20)(17,21)(18,19)(22,23,25,27,26,30,33,29)(24,31,34,28,32,35,37,36);(14,16,20,15,18,21,17,19)(23,27,30,29)(24,32)(28,31,36,35)(34,37);(15,19)(16,21)(22,24,33,37,26,32,25,34)(23,28,27,35,30,36,29,31)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2848);