Finite Group DatabasebetaFinite Group Databasebeta| order | 4970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×D71⋊C7 |
| unambiguous semidirect product | (C5×D71)⋊C7 |
| Fitting, socle, Hall | C5×C71 ⋊ C2×C7 |
| derived, Sylow | C71 ⋊ C2×C5×C7 |
| Hall | C5×C71⋊C7 ⋊ C2 |
| Hall | C5×D71 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C2×C5 |
| Hall | D71 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D71⋊C7 |
| commutator, hypocenter | C71 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C71 | C2×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
95 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×D71⋊C7, C5×C3⋊(D71⋊C7), C25×D71⋊C7, … |
| maximal normal subgroup of | C3×C5×D71⋊C7, C25×D71⋊C7, (D71⋊C7)⋊C25, … |
| maximal quotient of | C3×C5×D71⋊C7, C5×C3⋊(D71⋊C7), C25×D71⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4970, 12);