Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6652 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#6656 |
| Hall | C3×C52 ⋊ SD16 |
| Sylow | C52 ⋊ #215 |
| Sylow | C3 ⋊ C5×#687 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #72230768, C5×D3×#687, #72230787, … |
| maximal normal subgroup of | #72230768, C5×D3×#687, #72230787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 294);