Finite Group DatabasebetaFinite Group Databasebeta| order | 4970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C2×(C71⋊C5)⋊C7 |
| unambiguous semidirect product | (C2×C71⋊C5)⋊C7 |
| unambiguous semidirect product | (C2×C71⋊C7)⋊C5 |
| Fitting, socle, Hall | C2×C71 ⋊ C5×C7 |
| derived, Sylow | C71 ⋊ C2×C5×C7 |
| Hall | C2×C71⋊C7 ⋊ C5 |
| Hall | C2×C71⋊C5 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C2×C5 |
| Hall | C71⋊C5 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C71⋊C5)⋊C7 |
| commutator, hypocenter | C71 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C71 | C5×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
74 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4970, 4);