Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#17366 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C22×C22⋊C4 |
| prime radical | C22×C13×#41 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C42×C13 ◁ G | |
1246 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)(14,15,17,21,18,19,16,20)(22,23)(24,32,35,28)(25,29)(26,30)(27,31)(33,37,34,36);(22,24)(23,28)(25,33)(26,34)(27,35)(29,36)(30,37)(31,32);(15,19)(20,21)(22,25,27,26)(23,29,31,30)(24,33,35,34)(28,36,32,37);(14,16,18,17)(15,20,19,21)(22,26,27,25)(23,30,31,29)(24,34,35,33)(28,37,32,36)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10354);