Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #6758 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#91235 |
| Fitting | C2×C32×C4×C5 ⋊ C4 |
| Hall | C32×C5 ⋊ #95 |
| Sylow | C32 ⋊ (C2×AGL(1,𝔽5))⋊C4 |
| Sylow | C5 ⋊ C3×C3⋊#95 |
358 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72260236, C3×AGL(1,𝔽5)×(C2×D3)⋊C4, #72260267 |
| maximal normal subgroup of | #72260236, C3×AGL(1,𝔽5)×(C2×D3)⋊C4, #72260267 |
| maximal quotient of | C3×#11746737, C3×#11746733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2600);