Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, derived, Hall | C7×C169 ⋊ C32 |
| Sylow | C169 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C169 | C32 |
| Frattini | C13 | ΓL(1,𝔽8)×C13⋊C3 |
| socle | C7×C13 | C3×C13⋊C3 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
295 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×D169⋊C3, AGL(1,𝔽7)×C169⋊C3, ΓL(1,𝔽8)⋊(D169⋊C3), … |
| maximal normal subgroup of | ΓL(1,𝔽8)×D169⋊C3, AGL(1,𝔽7)×C169⋊C3, ΓL(1,𝔽8)⋊(D169⋊C3), … |
| maximal quotient of | C2×ΓL(1,𝔽8)×C169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 7);