Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×Dic3⋊AGL(1,𝔽5) |
| unambiguous semidirect product | Dic3⋊(C3×AGL(1,𝔽5)) |
| Hall | C32×C5 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×Dic3⋊C4 |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×Dic3⋊AGL(1,𝔽5), #13088407, #13088409, … |
| maximal normal subgroup of | D3×Dic3⋊AGL(1,𝔽5), #13088407, #13088409, … |
| maximal quotient of | C3×#91159, C3×#91160, C3×#91161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 427);