Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×(C2×D3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C2×D3)⋊(C5×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C5×D3) |
| Hall | C3×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ (C2×D3)⋊C4 |
| Sylow | C3 ⋊ C5×C22⋊AGL(1,𝔽5) |
146 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 146 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) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(C2×D3)⋊AGL(1,𝔽5), C5×D3×C22⋊AGL(1,𝔽5), #72230095 |
| maximal normal subgroup of | D5×(C2×D3)⋊AGL(1,𝔽5), C5×D3×C22⋊AGL(1,𝔽5), #72230095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 539);