Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13259 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #459 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1982 |
| prime radical | C13×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
472 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)(14,15,19,26,20,25,35,44,21,27,34,23,18,36,17,24)(16,28,32,42,31,43,30,39,33,38,29,22,37,40,45,41);(14,16,20,37,21,33,18,31)(15,22,25,39,27,42,36,41)(17,29,19,30,35,32,34,45)(23,38,24,43,26,28,44,40);(14,17,18,34,21,35,20,19)(15,23,25,24,27,26,36,44)(16,29,31,45,33,32,37,30)(22,38,39,43,42,28,41,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6247);