Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26481 |
| 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 | |
798 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)(28,39)(29,41)(30,34)(31,37)(32,36)(33,38)(35,40);(14,15)(16,17)(19,22)(23,24)(26,28,32,29,33,40,31,30)(27,34,37,35,38,41,36,39);(15,17)(26,29,31,28,33,30,32,40)(27,35,36,34,38,39,37,41);(18,20,21,25)(19,23,22,24)(26,30,31,40,33,29,32,28)(27,35,36,34,38,39,37,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19469);