Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C5 |
| direct product | C4×C41×C52⋊C3 |
| unambiguous semidirect product | (C4×C52)⋊(C3×C41) |
| unambiguous semidirect product | (C4×C52×C41)⋊C3 |
| Fitting, Hall | C4×C52×C41 ⋊ C3 |
| derived, Sylow | C52 ⋊ C3×C4×C41 |
| Hall | C52×C41 ⋊ C3×C4 |
| Hall | C4×C52 ⋊ C3×C41 |
36 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×C41×C52⋊C3, C3×C4×C41×C52⋊C3 |
| maximal normal subgroup of | C3×C4×C41×C52⋊C3 |
| maximal quotient of | C4×C41×C52⋊C9, Dic3×C41×C52⋊C3, C3×C4×C41×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 63);