Finite Group DatabasebetaFinite Group Databasebeta| order | 4970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D355 |
| unambiguous semidirect product | C5⋊(C7×D71) |
| Fitting, socle, Hall | C5×C7×C71 ⋊ C2 |
| derived, Hall | C5×C71 ⋊ C2×C7 |
| Hall | C7×C71 ⋊ D5 |
| Sylow | C71 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ D71 |
| Sylow | C5 ⋊ C7×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D355 |
| commutator, hypocenter | C5×C71 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C71 | C2 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
1253 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D355, C7×D1065, ΓL(1,𝔽8)×D355, … |
| maximal normal subgroup of | C3×C7×D355, ΓL(1,𝔽8)×D355, C7×C5⋊(D71⋊C5), … |
| maximal quotient of | C3×C7×D355, C7×D1065, C7×D1775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4970, 9);