Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1037 |
| derived, Hall | C17×C61 ⋊ C3×C4 |
| Hall | C3×C17×C61 ⋊ C4 |
| Hall | C3×C61 ⋊ Dic17 |
| Sylow | C61 ⋊ C3×Dic17 |
| Hall | C3×C17 ⋊ Dic61 |
| Sylow | C17 ⋊ C3×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1037 |
| commutator, hypocenter | C17×C61 | C3×C4 |
| Frattini | C2 | C3×D1037 |
| Fitting, socle, prime radical | C2×C3×C17×C61 | C2 |
| cosocle | C2×C17×C61 | C2×C3 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
3120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic1037, Dic1037⋊C9, C3×Dic1037⋊C3, … |
| maximal normal subgroup of | C9×Dic1037, Dic1037⋊C9, C3×Dic1037⋊C3, … |
| maximal quotient of | C9×Dic1037, C3×Dic3111, C32×Dic1037 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 5);