Finite Group DatabasebetaFinite Group Databasebeta| order | 12180 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C2 |
| direct product | A5×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C7×A5) |
| unambiguous semidirect product | (C29×A5)⋊C7 |
| Fitting, Sylow | C29 ⋊ C7×A5 |
| socle, derived, Hall | C29×A5 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C29×A5 | C7 |
| Fitting | C29 | C7×A5 |
| LCS | G ▷ C29×A5 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
55 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A5×C29⋊C7 |
| maximal normal subgroup of | C3×A5×C29⋊C7 |
| maximal quotient of | C3×A5×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12180, 166);