Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C22⋊(C52⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C4×C22⋊(C52⋊C3) |
| unambiguous semidirect product | (C22×C4)⋊(C52⋊C3) |
| unambiguous semidirect product | (C4×C52)⋊A4 |
| Fitting, Hall | C22×C4×C52 ⋊ C3 |
| derived | C22×C52 ⋊ C3×C4 |
| Sylow | C52 ⋊ C4×A4 |
| Sylow | C22×C4 ⋊ C52⋊C3 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 882);