Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,21)(16,24,26,39)(18,32,30,22)(19,23,31,38)(20,35,36,43)(25,33,37,27)(28,41,29,42)(34,45,44,40);(14,15)(16,25,28,20)(17,21)(18,22)(19,23)(24,27,41,43)(26,37,29,36)(30,32)(31,38)(33,42,35,39)(34,40)(44,45);(14,16,17,29)(15,20,21,37)(18,33,30,43)(19,28,31,26)(22,39,32,41)(23,25,38,36)(24,40,42,45)(27,34,35,44)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3365);