Finite Group DatabasebetaFinite Group Databasebeta| order | 9765 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C32×C31)⋊(C5×C7) |
| unambiguous semidirect product | (C32×C7×C31)⋊C5 |
| Fitting, socle, Hall | C32×C7×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C32×C5×C7 |
| Hall | C32×C31 ⋊ C5×C7 |
| Hall | C7×C31 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C32×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C7 | |
48 conjugacy classes of subgroups.
693 conjugacy classes — view the full character table.
| maximal subgroup of | C32×C7×D31⋊C5, C32×C7⋊(D31⋊C5), C32×D7×ΓL(1,𝔽32), … |
| maximal normal subgroup of | C32×C7×D31⋊C5, C32×C7⋊(D31⋊C5), C32×D7×ΓL(1,𝔽32), … |
| maximal quotient of | C2×C32×C7×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9765, 18);