Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18716 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1060 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)(15,18)(16,20)(19,21)(23,28)(25,26)(29,35)(30,34)(31,33)(36,37);(16,20)(18,21)(22,23,27,30)(24,29,32,37)(25,28,26,34)(31,36,33,35);(14,15)(16,21)(17,19)(18,20)(22,24)(23,29)(25,33)(26,31)(27,32)(28,35)(30,37)(34,36);(22,25,27,26)(23,28,30,34)(24,31,32,33)(29,36,37,35)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11704);