Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4×D25 |
| Fitting | C2×C3×C4×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C22×C3×C4 |
| Hall | C3×C25 ⋊ C22×C4 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C4×D25⋊C5, C2×C3×C4×#1035 |
| maximal normal subgroup of | C2×C3×C4×D25⋊C5, C2×C3×C4×#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 150);