Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×C4×#1043 |
| Fitting | C3×C4×C52 ⋊ C4 |
| derived, Sylow | C52 ⋊ C3×C42 |
| Hall | C3×C52 ⋊ C42 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×#1043⋊C3, C3×C4×#6053, C3×C8×#1043, … |
| maximal normal subgroup of | C3×C4×#1043⋊C3, C3×C4×#6053, C3×C8×#1043, … |
| maximal quotient of | C3×C8×#1043, C2×C3×C4×#1043, C3×Dic3×#1043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 711);