Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#23612 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
1214 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)(14,15,16,17)(22,23,27,31)(24,32,35,37)(25,30,26,29)(28,33,36,34);(18,19)(20,21)(22,24,26,34,27,35,25,33)(23,28,30,32,31,36,29,37);(15,17)(19,21)(23,29)(24,33)(25,26)(28,36)(30,31)(34,35);(22,25,27,26)(23,30,31,29)(24,33,35,34)(28,32,36,37)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16600);