Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C23×C42 |
| direct product | C13×#21817 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C22×C22⋊C4 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
1282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
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)(16,20)(17,19)(18,21)(22,23,26,30,27,25,34,29)(24,28,33,36,32,31,37,35);(14,16,17,21)(15,18,19,20)(22,24)(23,28)(25,31)(26,33)(27,32)(29,35)(30,36)(34,37);(16,21)(18,20)(22,25)(23,27)(24,31)(26,29)(28,32)(30,34)(33,35)(36,37);(15,19)(18,20)(24,32)(28,31)(33,37)(35,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14805);