Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C17⋊(D61⋊C3) |
| unambiguous semidirect product | (C2×C17)⋊(D61⋊C3) |
| unambiguous semidirect product | (C2×C61⋊C3)⋊D17 |
| unambiguous semidirect product | (C2×D1037)⋊C3 |
| Fitting, socle | C2×C17×C61 ⋊ C2×C3 |
| derived, Hall | C17×C61 ⋊ C22×C3 |
| Hall | C2×D1037 ⋊ C3 |
| Hall | C17×C61⋊C3 ⋊ C22 |
| Hall | C61⋊C3 ⋊ C2×D17 |
| Sylow | C61 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊(D61⋊C3) |
| commutator, cosocle, hypocenter | C17×C61 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C61 | C2×C3 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
400 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C17⋊(D61⋊C3), C2×C3×C17⋊(D61⋊C3), C2×C3⋊(C17⋊(D61⋊C3)) |
| maximal normal subgroup of | C2×C3×C17⋊(D61⋊C3) |
| maximal quotient of | C2×C17⋊(D61⋊C9), D3×C17⋊(D61⋊C3), C2×C3×C17⋊(D61⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 22);