Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17×C61 · Schur multiplier (H2) = C2 |
| direct product | A4×C17×C61 |
| unambiguous semidirect product | C22⋊(C3×C17×C61) |
| unambiguous semidirect product | (C22×C17)⋊(C3×C61) |
| Fitting, socle, Hall | C22×C17×C61 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C17×C61 |
| Hall | C22×C61 ⋊ C3×C17 |
| Hall | C22×C17 ⋊ C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C61 | A4 |
| commutator, cosocle, hypocenter | C22 | C3×C17×C61 |
| Frattini | C1 | G |
| Fitting, socle | C22×C17×C61 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C17×C61 | |
20 conjugacy classes of subgroups.
4148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | A4×C17×C61⋊C3, C3×A4×C17×C61 |
| maximal normal subgroup of | A4×C17×C61⋊C3, C3×A4×C17×C61 |
| maximal quotient of | C17×C22⋊C9×C61, C3×A4×C17×C61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 44);