Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63739 |
| Hall | C32×C5 ⋊ #102 |
| Sylow | C32 ⋊ C5×#102 |
180 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 38 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) = 240 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3,4,5)(6,8)(7,10,11)(12,13,14,15)(17,20)(18,23)(21,22);(6,7)(8,11)(9,10)(16,17)(18,20)(19,22)(21,23)150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1884);