Finite Group DatabasebetaFinite Group Databasebeta| order | 4970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D71⋊C5) |
| unambiguous semidirect product | (C71⋊C5)⋊D7 |
| unambiguous semidirect product | D497⋊C5 |
| Fitting, socle, derived, Hall | C7×C71 ⋊ C2×C5 |
| Hall | C7×C71⋊C5 ⋊ C2 |
| Hall | D497 ⋊ C5 |
| Hall | C71⋊C5 ⋊ D7 |
| Sylow | C71 ⋊ C5×D7 |
| Sylow | C7 ⋊ D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C71 | C2×C5 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,71|c^a=c^6,d^a=d^70,d^b=d^5474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4970, 17);