Finite Group DatabasebetaFinite Group Databasebeta| order | 945 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C9 · Schur multiplier (H2) = C3 |
| direct product | C5×C9×ΓL(1,𝔽8) |
| Fitting | C5×C7×C9 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C5×C9 |
| Hall | C5×C7 ⋊ C3×C9 |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 315 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9×AGL(1,𝔽7), C9×D5×ΓL(1,𝔽8), C9×C5⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | C5×C9×AGL(1,𝔽7), C9×D5×ΓL(1,𝔽8), C9×C5⋊AGL(1,𝔽7), … |
| maximal quotient of | C2×C5×C9×ΓL(1,𝔽8) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(945, 3);