Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
756 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)(20,25)(21,23)(22,24)(26,27,32,40,31,36,30,35)(28,33,29,39,38,34,37,41);(14,15)(16,17)(18,20,22,21)(19,23,24,25)(26,28)(27,33)(29,32)(30,37)(31,38)(34,36)(35,41)(39,40);(15,17)(18,21,22,20)(19,23,24,25)(26,29,31,37)(27,34,36,33)(28,30,38,32)(35,41,40,39);(19,24)(23,25)(26,30,31,32)(27,35,36,40)(28,29,38,37)(33,39,34,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17607);