Finite Group DatabasebetaFinite Group Databasebeta| order | 7347 |
| isoclinism | isoclinic class of C79⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C79⋊C3 |
| unambiguous semidirect product | C79⋊(C3×C31) |
| Fitting, socle, Hall | C31×C79 ⋊ C3 |
| derived, Sylow | C79 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C79⋊C3 |
| commutator, hypocenter | C79 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C79 | C3 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
899 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×C79⋊C3, C31×D79⋊C3, D31×C79⋊C3, … |
| maximal normal subgroup of | C2×C31×C79⋊C3, C31×D79⋊C3, D31×C79⋊C3, … |
| maximal quotient of | C2×C31×C79⋊C3, C31×C79⋊C9, C3×C31×C79⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7347, 2);