Finite Group DatabasebetaFinite Group Databasebeta| order | 7686 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C7×C61⋊C3 |
| unambiguous semidirect product | (C2×C61)⋊(C32×C7) |
| unambiguous semidirect product | (C2×C3×C61)⋊(C3×C7) |
| Fitting, socle | C2×C3×C7×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C2×C32×C7 |
| Hall | C2×C7×C61 ⋊ C32 |
| Hall | C7×C61 ⋊ C2×C32 |
| Hall | C2×C61 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | C61⋊C3 |
| commutator, hypocenter | C61 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C3×C7 | |
48 conjugacy classes of subgroups.
966 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7686, 58);