Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25171 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
1072 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,20)(22,23,27,31)(24,30,26,28)(25,33,34,36)(29,35,37,32);(14,15)(16,17)(18,20,21,19)(23,28)(24,26)(25,34)(29,36)(30,31)(33,37);(15,17)(19,20)(22,24,27,26)(23,28,31,30)(25,32,34,35)(29,33,37,36);(22,25,27,34)(23,29,31,37)(24,32,26,35)(28,33,30,36)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18159);