Finite Group DatabasebetaFinite Group Databasebeta| order | 12612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C1051 ⋊ C2×C3 |
| derived, Sylow | C1051 ⋊ C22×C3 |
| Hall | C2×D1051 ⋊ C3 |
| Hall | C1051⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1051⋊C3 |
| commutator, cosocle, hypocenter | C1051 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1051 | C2×C3 |
| LCS | G ▷ C1051 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
362 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D1051⋊C3, C2×C3×D1051⋊C3, C2×C3⋊(D1051⋊C3) |
| maximal normal subgroup of | C2×C3×D1051⋊C3 |
| maximal quotient of | C2×D1051⋊C9, D3×D1051⋊C3, C2×C3×D1051⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12612, 8);