Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×C4×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C2×C4×C5⋊D5)⋊C3 |
| Fitting | C2×C4×C52 ⋊ C2×C3 |
| derived, Sylow | C52 ⋊ C22×C3×C4 |
| Hall | C2×C4×C5⋊D5 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C22×C4 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 684);