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×#25054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3061 | 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)(24,28)(25,32)(26,30)(27,31)(29,36)(33,35)(34,37);(14,16,17,20)(15,18,19,21)(22,24,26,32,27,34,36,33)(23,25,29,28,31,35,30,37);(15,19)(18,21)(22,24)(23,28)(25,30)(26,32)(27,34)(29,35)(31,37)(33,36);(22,25,26,28,27,35,36,37)(23,24,29,32,31,34,30,33)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18042);