Finite Group DatabasebetaFinite Group Databasebeta| order | 7567 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C7×C47⋊C23 |
| unambiguous semidirect product | C47⋊(C7×C23) |
| unambiguous semidirect product | (C7×C47)⋊C23 |
| Fitting, socle, Hall | C7×C47 ⋊ C23 |
| derived, Sylow | C47 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C47⋊C23 |
| commutator, hypocenter | C47 | C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C7 | |
8 conjugacy classes of subgroups.
175 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7×C47⋊C23, C7×AGL(1,𝔽47), D7×C47⋊C23, … |
| maximal normal subgroup of | C2×C7×C47⋊C23, C7×AGL(1,𝔽47), D7×C47⋊C23, … |
| maximal quotient of | C2×C7×C47⋊C23, C3×C7×C47⋊C23, C5×C7×C47⋊C23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7567, 1);