Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
742 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)(16,19)(17,21)(18,20)(22,23)(24,33)(25,30)(26,35)(27,34)(28,31)(29,32)(36,37);(14,16,18,17)(15,19,20,21)(22,24,29,36)(23,26,32,25)(27,30,28,35)(31,37,34,33);(14,17,18,16)(15,19,20,21)(22,25,29,26)(23,30,32,35)(24,34,36,31)(27,37,28,33);(22,26,29,25)(23,24,32,36)(27,37,28,33)(30,34,35,31)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19185);