Finite Group DatabasebetaFinite Group Databasebeta| order | 4970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽71) |
| unambiguous semidirect product | (D71⋊C5)⋊C7 |
| unambiguous semidirect product | (D71⋊C7)⋊C5 |
| unambiguous semidirect product | ((C71⋊C5)⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C71 ⋊ C2×C5×C7 |
| Hall | (C71⋊C5)⋊C7 ⋊ C2 |
| Hall | D71⋊C7 ⋊ C5 |
| Hall | D71⋊C5 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C2×C5 |
| Hall | C71⋊C5 ⋊ C2×C7 |
| Hall | D71 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C71 | C2×C5×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,71|d^a=d^70,d^b=d^54,d^c=d^4571 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4970, 18);