Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#9690 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
456 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)(15,17)(19,22,23,24)(26,27,31,34,30,33,29,39)(28,35,38,40,36,41,37,32);(18,19,20,24,21,23,25,22)(26,28,30,36)(27,32)(29,37,31,38)(33,40)(34,35)(39,41);(14,15,16,17)(27,33)(28,36)(34,39)(37,38)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2678);