Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26906 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
870 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)(26,27,29,34,31,35,30,32)(28,36,37,33,39,40,38,41);(14,15)(16,17)(19,22)(23,24)(27,32)(29,30)(33,40)(34,35)(36,41)(37,38);(15,17)(26,28,31,39)(27,33,35,41)(29,38,30,37)(32,40,34,36);(18,20,21,25)(19,23,22,24)(27,34)(29,30)(32,35)(33,36)(37,38)(40,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19894);