Finite Group DatabasebetaFinite Group Databasebeta| order | 6958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×D71⋊C7 |
| unambiguous semidirect product | D71⋊C72 |
| unambiguous semidirect product | (C71⋊C7)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D71)⋊C7 |
| Fitting, socle | C7×C71 ⋊ C2×C7 |
| derived, Sylow | C71 ⋊ C2×C72 |
| Hall | C7×C71⋊C7 ⋊ C2 |
| Hall | D71 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D71⋊C7 |
| commutator, hypocenter | C71 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C71 | C2×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
133 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D71⋊C7, C2×C7×D71⋊C7, ΓL(1,𝔽8)×D71⋊C7, … |
| maximal normal subgroup of | D7×D71⋊C7, C2×C7×D71⋊C7, ΓL(1,𝔽8)×D71⋊C7, … |
| maximal quotient of | C7×Dic71⋊C7, C2×C7×D71⋊C7, C3×C7×D71⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6958, 8);