Finite Group DatabasebetaFinite Group Databasebeta| order | 12078 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| Fitting, socle | C3×C11×C61 ⋊ C2×C3 |
| derived | C3×C61 ⋊ C2×C3×C11 |
| Hall | C3×C11×C61⋊C3 ⋊ C2 |
| Hall | C11×C61 ⋊ C3×D3 |
| Hall | C3×C61⋊C3 ⋊ C2×C11 |
| Sylow | C61 ⋊ C3×D3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(D61⋊C3) |
| commutator, cosocle, hypocenter | C3×C61 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C61 | C2×C3 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C11 | |
36 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C11×D61⋊C3, D11×C3⋊(D61⋊C3), D33⋊(D61⋊C3), … |
| maximal normal subgroup of | D3×C11×D61⋊C3, D11×C3⋊(D61⋊C3), D33⋊(D61⋊C3), … |
| maximal quotient of | C11×C3⋊(Dic61⋊C3), C2×C11×C3⋊(D61⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12078, 17);