Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10057 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(19,22)(20,24)(23,25)(26,27,31,34)(28,35,37,40)(29,33,30,38)(32,39,41,36);(14,15)(16,17)(20,24)(22,25)(26,28,31,37)(27,32,34,41)(29,36,30,39)(33,40,38,35);(15,17)(18,19)(20,25)(21,23)(22,24)(26,29,31,30)(27,33,34,38)(28,36,37,39)(32,40,41,35)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3045);