Finite Group DatabasebetaFinite Group Databasebeta| order | 12180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1015 |
| unambiguous semidirect product | (C5×D3)⋊D203 |
| unambiguous semidirect product | (D3×C7)⋊D145 |
| unambiguous semidirect product | (D3×C29)⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C29 | C22 |
| LCS | G ▷ C3×C5×C7×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
1527 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D1015, D3×C5⋊(ΓL(1,𝔽8)⋊D29), C3×D3×D1015, … |
| maximal normal subgroup of | D3×C5⋊(ΓL(1,𝔽8)⋊D29), C3×D3×D1015 |
| maximal quotient of | D9×D1015, C3×D3×D1015, D3×D3045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12180, 141);