Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25915 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2619 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
1110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,22,25)(20,24,21,23)(27,31)(28,35)(29,36)(32,39)(37,41)(38,40);(14,15)(16,17)(18,20,22,21)(19,23,25,24)(26,27,30,31)(28,32,37,38)(29,34,36,33)(35,40,41,39);(15,17)(18,20,22,21)(19,24,25,23)(26,28,36,41,30,37,29,35)(27,32,33,39,31,38,34,40);(18,21,22,20)(19,24,25,23)(26,29,30,36)(27,33,31,34)(28,35,37,41)(32,39,38,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18903);