Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26272 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3155 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
800 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)(16,20)(17,18)(19,21)(22,23,28,32)(24,33,36,26)(25,37,31,27)(29,30,34,35);(15,18)(19,20)(22,24,27,35,28,36,37,30)(23,29,31,33,32,34,25,26);(22,25,27,23,28,31,37,32)(24,34,35,26,36,29,30,33);(14,16,17,21)(15,19,18,20)(22,26,37,34,28,33,27,29)(23,30,25,36,32,35,31,24)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19260);