Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26845 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
806 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)(26,27,32,38)(28,39,41,35)(29,33,40,34)(30,37,31,36);(14,15)(16,17)(18,20,22,21)(19,23,24,25)(26,28,30,29,32,41,31,40)(27,33,36,39,38,34,37,35);(15,17)(18,21,22,20)(19,23,24,25)(26,28,30,29,32,41,31,40)(27,34,36,35,38,33,37,39);(19,24)(23,25)(26,29,30,41,32,40,31,28)(27,35,36,33,38,39,37,34)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19833);