Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#25055 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3060 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
724 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)(16,18)(17,19)(20,21)(22,23)(24,34)(25,36)(26,37)(27,33)(28,32)(29,35)(30,31);(14,16,17,20)(15,18,19,21)(22,24,28,36,27,31,26,35)(23,29,37,30,33,25,32,34);(15,19)(18,21)(22,24)(23,30)(25,37)(26,35)(27,31)(28,36)(29,32)(33,34);(22,25,28,34,27,29,26,30)(23,31,37,35,33,24,32,36)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18043);