Finite Group DatabasebetaFinite Group Databasebeta| order | 5838 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C139 ⋊ C2×C3 |
| Hall | #15668589 ⋊ C2 |
| Hall | C7×D139 ⋊ C3 |
| Hall | D139 ⋊ ΓL(1,𝔽8) |
| Sylow | C139 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C139 | C2×C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,139|d^a=d^138,c^b=c^2,d^b=d^96171 conjugacy classes — view the full character table.
| maximal subgroup of | #19154245⋊C2, C2×#19154245, ΓL(1,𝔽8)×D139⋊C3, … |
| maximal normal subgroup of | #19154245⋊C2, C2×#19154245, ΓL(1,𝔽8)×D139⋊C3, … |
| maximal quotient of | #26043014, C2×#19154245, #31776102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5838, 15);