Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D17×D61 |
| Fitting, socle, Hall | C3×C17×C61 ⋊ C22 |
| derived, Hall | C17×C61 ⋊ C22×C3 |
| Hall | C3×C61 ⋊ C2×D17 |
| Sylow | C61 ⋊ C2×C3×D17 |
| Hall | C3×C17 ⋊ C2×D61 |
| Sylow | C17 ⋊ C2×C3×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×D61 |
| commutator, cosocle, hypocenter | C17×C61 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C61 | C22 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
960 conjugacy classes — view the full character table.
| maximal subgroup of | D17×D61⋊C9, C9×D17×D61, C3×D17×D61⋊C3, … |
| maximal normal subgroup of | D17×D61⋊C9, C9×D17×D61, C3×D17×D61⋊C3, … |
| maximal quotient of | C9×D17×D61, C32×D17×D61, C3×D51×D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 30);