Finite Group DatabasebetaFinite Group Databasebeta| order | 7526 |
| automorphism | Aut(G) order 13697320 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3763 |
| unambiguous semidirect product | C53⋊D71 |
| unambiguous semidirect product | C71⋊D53 |
| Fitting, socle, derived, Hall | C53×C71 ⋊ C2 |
| Sylow | C71 ⋊ D53 |
| Sylow | C53 ⋊ D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53×C71 | C2 |
| LCS | G ▷ C53×C71 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,53,71|b^a=b^52,c^a=c^701883 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×D71, C2×D3763, C3×D3763, … |
| maximal normal subgroup of | D53×D71, C2×D3763, C3×D3763, … |
| maximal quotient of | Dic3763, C2×D3763, C3×D3763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7526, 3);