Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of Dic110 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×C22⋊D55 |
| Fitting | C22×C3×C5×C11 ⋊ C2 |
| Hall | C3×C5×C11 ⋊ D4 |
| Hall | C5×C11 ⋊ C3×D4 |
| Hall | C3×C11 ⋊ C22⋊D5 |
| Hall | C3×C5 ⋊ C22⋊D11 |
| Sylow | C11 ⋊ C3×C22⋊D5 |
| Sylow | C5 ⋊ C3×C22⋊D11 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 660 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(15,16,18,19,17)(21,23);(5,6)(7,8)(9,10)(11,12)(13,14)(16,17)(18,19)(20,21)(22,23)339 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 109);