Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×C7⋊C9 |
| unambiguous semidirect product | C7⋊(C9×C132) |
| derived, Sylow | C7 ⋊ C9×C132 |
| Hall | C7×C132 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C132 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C9×C132 |
| Frattini | C3 | C132×ΓL(1,𝔽8) |
| Fitting, socle, prime radical | C3×C7×C132 | C3 |
| cosocle | C3×C7 | C3×C132 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C132 | |
96 conjugacy classes of subgroups.
2535 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C132×D7⋊C9, C13×(C7⋊C9)⋊D13, (C7⋊C9)⋊(C13⋊D13), … |
| maximal normal subgroup of | C132×D7⋊C9, C13×(C7⋊C9)⋊D13, (C7⋊C9)⋊(C13⋊D13), … |
| maximal quotient of | C2×C132×C7⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 18);