Finite Group DatabasebetaFinite Group Databasebeta| order | 12246 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C157 · Schur multiplier (H2) = C1 |
| direct product | D13⋊C3×C157 |
| unambiguous semidirect product | D13⋊(C3×C157) |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×C157) |
| Fitting, socle, Hall | C13×C157 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C2×C3×C157 |
| Hall | C13⋊C3×C157 ⋊ C2 |
| Hall | D13×C157 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C157 |
| Hall | D13 ⋊ C3×C157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C157 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C157 |
| Frattini | C1 | G |
| Fitting, socle | C13×C157 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C157 | |
16 conjugacy classes of subgroups.
1256 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽13)×C157, #37587605, D13⋊C3×D157, … |
| maximal normal subgroup of | AGL(1,𝔽13)×C157, #37587605, D13⋊C3×D157, … |
| maximal quotient of | Dic13⋊C3×C157, C2×D13⋊C3×C157, C157×D13⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12246, 23);