Finite Group DatabasebetaFinite Group Databasebeta| order | 12246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D471 |
| unambiguous semidirect product | C3⋊(C13×D157) |
| Fitting, socle, Hall | C3×C13×C157 ⋊ C2 |
| derived, Hall | C3×C157 ⋊ C2×C13 |
| Hall | C13×C157 ⋊ D3 |
| Sylow | C157 ⋊ D3×C13 |
| Hall | C3×C13 ⋊ D157 |
| Sylow | C3 ⋊ C13×D157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D471 |
| commutator, cosocle, hypocenter | C3×C157 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C157 | C2 |
| LCS | G ▷ C3×C157 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
3081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D157, D13×D471, D39⋊D157, … |
| maximal normal subgroup of | D3×C13×D157, D13×D471, D39⋊D157, … |
| maximal quotient of | C13×Dic471, C2×C13×D471, C13×D1413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12246, 12);