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×#24718 |
| 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 | |
746 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)(18,19,21,22)(20,24,25,23)(26,27,30,36,31,35,40,34)(28,37,39,33,29,32,38,41);(14,15)(16,17)(19,22)(23,24)(26,28)(27,32)(29,31)(30,39)(33,34)(35,37)(36,41)(38,40);(15,17)(26,29,31,28)(27,33,35,41)(30,39,40,38)(32,36,37,34);(18,20,21,25)(19,23,22,24)(26,30,31,40)(27,34,35,36)(28,38,29,39)(32,41,37,33)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17706);