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×D220 |
| unambiguous semidirect product | C4⋊(C3×D55) |
| Fitting | C3×C4×C5×C11 ⋊ C2 |
| Hall | C3×C5×C11 ⋊ D4 |
| Hall | C5×C11 ⋊ C3×D4 |
| Hall | C3×C11 ⋊ D20 |
| Hall | C3×C5 ⋊ D44 |
| Sylow | C11 ⋊ C3×D20 |
| Sylow | C5 ⋊ C3×D44 |
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)(4,5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23);(5,7)(9,12)(10,11)(14,23)(15,22)(16,21)(17,20)(18,19)339 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 107);