Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#63926 |
| Fitting | C32×C5×D4 ⋊ C22 |
| Hall | C32×C5 ⋊ C2×D8 |
| Sylow | C32 ⋊ C2×C5×D8 |
358 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 358 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) = 19 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3,4,5)(6,7)(8,13)(9,11)(10,12)(14,15,16)(17,18,19);(7,10)(8,12)(11,13)(15,16);(7,10)(8,12)(11,13)(18,19)165 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#63926, C5×#10595100, #72230428 |
| maximal normal subgroup of | D5×#63926, C5×#10595100, #72230428 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3515);