Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#6777 |
| Fitting | C3×C4×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ D3×D4 |
| Sylow | C3 ⋊ C5×D4×D5 |
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | #72230978, C5×D3×D4×D5, D5×#6777, … |
| maximal normal subgroup of | #72230978, C5×D3×D4×D5, D5×#6777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 789);