Finite Group DatabasebetaFinite Group Databasebeta| order | 7514 |
| automorphism | Aut(G) order 12262848 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3757 |
| unambiguous semidirect product | C13⋊D289 |
| unambiguous semidirect product | C289⋊D13 |
| Fitting, derived, Hall | C13×C289 ⋊ C2 |
| Sylow | C289 ⋊ D13 |
| Sylow | C13 ⋊ D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C289 | C2 |
| Frattini | C17 | D221 |
| socle | C13×C17 | D17 |
| LCS | G ▷ C13×C289 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,17^2|c^17=d^16,b^a=b^12,c^a=c^16d,d^a=d^161880 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28418607, #28418608, D13×D289, … |
| maximal normal subgroup of | #28418607, #28418608, D13×D289, … |
| maximal quotient of | Dic3757, C2×D3757, C3×D3757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7514, 4);