Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#25868 |
| 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 ◁ C2×C13×#117 ◁ G | |
1230 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)(20,24)(21,23)(22,25)(26,27,30,33)(28,35,37,32)(29,38,40,41)(31,36,39,34);(14,15)(16,17)(18,20,22,21)(19,23,25,24)(26,28,30,37)(27,32,33,35)(29,34,40,36)(31,38,39,41);(15,17)(18,20,22,21)(19,24,25,23)(26,29,39,35,30,40,31,32)(27,28,36,41,33,37,34,38);(18,21,22,20)(19,24,25,23)(27,33)(28,37)(34,36)(38,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18856);