Finite Group DatabasebetaFinite Group Databasebeta| order | 7010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D701⋊C5 |
| unambiguous semidirect product | (C701⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C701 ⋊ C2×C5 |
| Hall | C701⋊C5 ⋊ C2 |
| Hall | D701 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C701 | C2×C5 |
| LCS | G ▷ C701 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,701|c^a=c^700,c^b=c^21080 conjugacy classes — view the full character table.
| maximal subgroup of | #14584149⋊C5, C2×D701⋊C5, C3×D701⋊C5, … |
| maximal normal subgroup of | #14584149⋊C5, C2×D701⋊C5, C3×D701⋊C5, … |
| maximal quotient of | Dic701⋊C5, C2×D701⋊C5, C3×D701⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7010, 1);