Finite Group DatabasebetaFinite Group Databasebeta| order | 710 |
| isoclinism | isoclinic class of D71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D71⋊C5 |
| unambiguous semidirect product | (C71⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C71 ⋊ C2×C5 |
| Hall | C71⋊C5 ⋊ C2 |
| Hall | D71 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C71 | C2×C5 |
| LCS | G ▷ C71 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 71 |
Polycyclic presentation:
2,5,71|c^a=c^70,c^b=c^5417 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D71⋊C5, C3×D71⋊C5, C3⋊(D71⋊C5), … |
| maximal normal subgroup of | C2×D71⋊C5, C3×D71⋊C5, C5×D71⋊C5, … |
| maximal quotient of | Dic71⋊C5, C2×D71⋊C5, C3×D71⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(710, 1);