Finite Group DatabasebetaFinite Group Databasebeta| order | 18669 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C127⋊C7 |
| unambiguous semidirect product | C7⋊(C3×C127⋊C7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)×C127)⋊C7 |
| Fitting, socle, derived | C7×C127 ⋊ C3×C7 |
| Hall | C7×C127⋊C7 ⋊ C3 |
| Sylow | C127 ⋊ C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C127 | C3×C7 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 889 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊(D127⋊C7), AGL(1,𝔽7)×C127⋊C7, ΓL(1,𝔽8)×D127⋊C7, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(D127⋊C7), AGL(1,𝔽7)×C127⋊C7, ΓL(1,𝔽8)×D127⋊C7, … |
| maximal quotient of | C2×ΓL(1,𝔽8)×C127⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18669, 12);