Finite Group DatabasebetaFinite Group Databasebeta| order | 6958 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C2×C71⋊C49 |
| unambiguous semidirect product | (C2×C71)⋊C49 |
| derived, Sylow | C71 ⋊ C2×C49 |
| Hall | C2×C71 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C71⋊C7 |
| commutator, hypocenter | C71 | C2×C49 |
| Frattini | C7 | C2×C71⋊C7 |
| Fitting, socle | C2×C7×C71 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
| maximal subgroup of | Dic71⋊C49, C4×C71⋊C49, C2×D71⋊C49, … |
| maximal normal subgroup of | Dic71⋊C49, C4×C71⋊C49, C2×D71⋊C49, … |
| maximal quotient of | C4×C71⋊C49, C22×C71⋊C49, C2×C3×C71⋊C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6958, 3);