Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#63567 |
| Hall | C32×C5 ⋊ #103 |
| Sylow | C32 ⋊ C5×#103 |
206 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3,4,5)(6,8,9,7)(10,11,12,14,13,15,16,17)(19,20)(21,22,23);(6,7,9,8)(11,14)(12,16)(15,17)(18,19,20)(22,23)240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1109);