Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×D3×Dic10 |
| unambiguous semidirect product | (C5×D3)⋊(C5×Q8) |
| Hall | C3×C52 ⋊ C2×Q8 |
| Sylow | C52 ⋊ D3×Q8 |
| Sylow | C3 ⋊ C2×C5×Dic10 |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87872, C5×D3×#709, D3×#87871, … |
| maximal normal subgroup of | D3×#87872, C5×D3×#709, D3×#87871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 779);