Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13291 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1993 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
306 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)(16,27,31,43)(17,33,36,41)(18,37)(19,24)(20,26)(21,22,35,40)(23,28)(25,39)(29,38)(30,34,32,45)(42,44);(14,16,28,41,39,30,18,22,20,31,44,33,19,32,38,40)(15,21,29,45,24,36,42,43,26,35,37,34,25,17,23,27);(14,17,20,36)(15,22)(16,29)(18,34,38,45)(19,35,39,21)(23,32)(24,33)(25,41)(26,40)(27,28,43,44)(30,42)(31,37)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6279);