Finite Group DatabasebetaFinite Group Databasebeta| order | 13244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic301 |
| unambiguous semidirect product | C7⋊(C11×Dic43) |
| unambiguous semidirect product | C43⋊(C11×Dic7) |
| derived, Hall | C7×C43 ⋊ C4×C11 |
| Hall | C7×C11×C43 ⋊ C4 |
| Hall | C11×C43 ⋊ Dic7 |
| Hall | C7×C11 ⋊ Dic43 |
| Sylow | C43 ⋊ C11×Dic7 |
| Sylow | C7 ⋊ C11×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D301 |
| commutator, hypocenter | C7×C43 | C4×C11 |
| Frattini | C2 | C11×D301 |
| Fitting, socle | C2×C7×C11×C43 | C2 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
3344 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13244, 7);