Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C17×C61 ⋊ C22×C3 |
| Hall | D17×D61 ⋊ 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, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C61 | C22×C3 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D17×D61⋊C3, D51×D61⋊C3, D17×C3⋊(D61⋊C3), … |
| maximal normal subgroup of | C3×D17×D61⋊C3 |
| maximal quotient of | D17×D61⋊C9, C3×D17×D61⋊C3, D51×D61⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 20);