Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#21151 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C22×D4 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
1038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
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)(16,17)(18,19,21,20)(22,23)(24,31)(25,29)(26,35)(27,30)(28,33)(32,36)(34,37);(15,17)(18,20,21,19);(22,24,26,33,27,34,25,32)(23,28,29,31,30,36,35,37);(22,25,27,26)(23,29,30,35)(24,32,34,33)(28,31,36,37)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14139);