Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C4×D5×C3⋊Dic3 |
| derived, Hall | C32×C5 ⋊ C2×C42 |
| Sylow | C32 ⋊ C42×D5 |
| Sylow | C5 ⋊ C2×C4×C3⋊Dic3 |
648 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C42×D5×C3⋊D3, C4×AGL(1,𝔽5)×C3⋊Dic3, D5×#64149, … |
| maximal normal subgroup of | C42×D5×C3⋊D3, C4×AGL(1,𝔽5)×C3⋊Dic3, D5×#64149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3174);