Finite Group DatabasebetaFinite Group Databasebeta| order | 13244 |
| automorphism | Aut(G) order 16687440 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D6622 |
| direct product | C2×D3311 |
| unambiguous semidirect product | (C2×C7)⋊D473 |
| unambiguous semidirect product | (C2×C11)⋊D301 |
| unambiguous semidirect product | (C2×C43)⋊D77 |
| Fitting, socle | C2×C7×C11×C43 ⋊ C2 |
| derived, Hall | C7×C11×C43 ⋊ C22 |
| Hall | C11×C43 ⋊ C2×D7 |
| Hall | C7×C43 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D77 |
| Sylow | C11 ⋊ C2×D301 |
| Sylow | C7 ⋊ C2×D473 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3311 |
| commutator, hypocenter | C7×C11×C43 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C11×C43 | C2 |
| LCS | G ▷ C7×C11×C43 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
3314 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13244 |
| maximal normal subgroup of | D13244 |
| maximal quotient of | D13244, Dic6622 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13244, 26);