Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×#13108 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #387 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1917 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C8×C13 ◁ G | |
246 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)(14,15,19,26,20,24,38,43,21,25,39,27,18,34,36,30)(16,17,23,33,28,22,40,41,29,32,42,37,35,31,45,44);(14,16,19,23,20,28,38,40,21,29,39,42,18,35,36,45)(15,22,26,41,24,32,43,37,25,31,27,44,34,17,30,33);(14,17,18,31,21,32,20,22)(15,23,24,40,25,42,34,45)(16,27,28,30,29,26,35,43)(19,37,36,41,39,33,38,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6096);