Finite Group DatabasebetaFinite Group Databasebeta| order | 6958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | D7×C71⋊C7 |
| unambiguous semidirect product | C7⋊(C2×C71⋊C7) |
| unambiguous semidirect product | (D7×C71)⋊C7 |
| Fitting, socle, derived | C7×C71 ⋊ C2×C7 |
| Hall | C7×C71⋊C7 ⋊ C2 |
| Sylow | C71 ⋊ C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C71 | C2×C7 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
85 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D71⋊C7, C2×D7×C71⋊C7, AGL(1,𝔽7)×C71⋊C7, … |
| maximal normal subgroup of | D7×D71⋊C7, C2×D7×C71⋊C7, AGL(1,𝔽7)×C71⋊C7, … |
| maximal quotient of | Dic7×C71⋊C7, C2×D7×C71⋊C7, C3×D7×C71⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6958, 10);