Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C2×C43 |
| direct product | C13×#14677 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(22,23,26,24)(25,27,29,28)(30,31)(32,34)(33,35)(36,37);(15,17)(18,19,20,21)(23,24)(25,29)(31,32)(35,36);(14,15,16,17)(22,24,26,23)(25,27,29,28)(30,32,34,31)(33,35,37,36);(22,25,26,29)(23,27,24,28)(30,33,34,37)(31,35,32,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 7665);