Finite Group DatabasebetaFinite Group Databasebeta| order | 13244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(Dic43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊Dic11 |
| unambiguous semidirect product | Dic473⋊C7 |
| derived, Hall | C11×C43 ⋊ C4×C7 |
| Hall | C11×C43⋊C7 ⋊ C4 |
| Hall | Dic473 ⋊ C7 |
| Hall | C43⋊C7 ⋊ Dic11 |
| Sylow | C43 ⋊ C7×Dic11 |
| Sylow | C11 ⋊ Dic43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(D43⋊C7) |
| commutator, hypocenter | C11×C43 | C4×C7 |
| Fitting, socle | C2×C11×C43 | C2×C7 |
| LCS | G ▷ C11×C43 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,11,43,2|a^2=e,c^a=c^10,d^a=d^42,d^b=d^41164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13244, 12);