Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C169 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×C169 |
| unambiguous semidirect product | C7⋊(C9×C169) |
| derived, Sylow | C7 ⋊ C9×C169 |
| Hall | C7×C169 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C169 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C9×C169 |
| Frattini | C3×C13 | C13×ΓL(1,𝔽8) |
| Fitting | C3×C7×C169 | C3 |
| socle, prime radical, cosocle | C3×C7×C13 | C3×C13 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C169 | |
18 conjugacy classes of subgroups.
2535 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊C9×D169, D7⋊C9×C169, (C7⋊C9)⋊D169, … |
| maximal normal subgroup of | C7⋊C9×D169, D7⋊C9×C169, (C7⋊C9)⋊D169, … |
| maximal quotient of | C2×C7⋊C9×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 2);