Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#26137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2414 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G | |
894 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)(14,15)(16,17)(18,19)(20,23)(21,25)(22,24)(26,27,31,30)(28,32,35,38)(29,33,37,39)(34,40,41,36);(15,17)(18,20,22,21)(19,23,24,25)(26,28)(27,32)(29,36)(30,38)(31,35)(33,34)(37,40)(39,41);(18,21,22,20)(19,23,24,25)(26,29,31,37)(27,33,30,39)(28,34,35,41)(32,40,38,36);(15,17)(26,27,31,30)(28,32,35,38)(29,33,37,39)(34,40,41,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19125);