Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#704 |
| Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ C3×M16 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11717347, C5×D3×#704, #72231061, … |
| maximal normal subgroup of | C3×#11717347, C5×D3×#704, #72231061 |
| maximal quotient of | C3×C5×#6762 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 707);