Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#6654 |
| Hall | C3×C52 ⋊ D8 |
| Sylow | C52 ⋊ D24 |
| Sylow | C3 ⋊ C5×#686 |
120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 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 | #72229609, C5×D3×#686, #72230841, … |
| maximal normal subgroup of | #72229609, C5×D3×#686, #72230841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 292);