Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26824 |
| 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 | |
814 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)(28,35)(29,34)(30,40)(31,37)(32,36)(33,38)(39,41);(14,15)(16,17)(18,20,22,21)(19,23,24,25)(26,28,31,29,33,39,32,30)(27,34,36,35,38,40,37,41);(15,17)(18,21,22,20)(19,23,24,25)(26,29,31,39,33,30,32,28)(27,35,36,40,38,41,37,34);(19,24)(23,25)(26,30,32,39,33,29,31,28)(27,35,37,34,38,41,36,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19812);