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) = C22 |
| direct product | C3×(C2×D3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C2×D3)⋊(C3×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C3×D3) |
| Hall | C32×C5 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×(C2×D3)⋊C4 |
152 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 152 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×(C2×D3)⋊AGL(1,𝔽5), #13088405, #13088408, … |
| maximal normal subgroup of | D3×(C2×D3)⋊AGL(1,𝔽5), #13088405, #13088408, … |
| maximal quotient of | C3×#91151, C3×#91152, C3×#91153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 426);