Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26986 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
880 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)(26,27,31,35)(28,36,37,33)(29,32,38,41)(30,39,40,34);(14,15)(16,17)(18,20,21,25)(19,22,23,24)(26,28,30,29,31,37,40,38)(27,32,34,36,35,41,39,33);(15,17)(19,23)(22,24)(28,37)(29,38)(32,41)(33,36);(19,23)(22,24)(26,29,30,37,31,38,40,28)(27,33,34,32,35,36,39,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19974);