Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#686 |
| Fitting | C3×C52×D4 ⋊ C2 |
| Hall | C3×C52 ⋊ D8 |
| Sylow | C52 ⋊ C3×D8 |
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) = 120 |
255 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11717044, C5×D3×#686, #72230837, … |
| maximal normal subgroup of | C3×#11717044, C5×D3×#686, #72230837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 396);