Finite Group DatabasebetaFinite Group Databasebeta| order | 8757 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#15668589 |
| Fitting, socle | C3×C7×C139 ⋊ C3 |
| derived, Hall | C7×C139 ⋊ C32 |
| Sylow | C139 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15668589 |
| commutator, hypocenter | C7×C139 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C139 | C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
981 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19154253, C3×#19154249, C3×#19154245, … |
| maximal normal subgroup of | C3×#19154253, C3×#19154249, C3×#19154245, … |
| maximal quotient of | C2×C3×#15668589, A4×#15668589, C3×C22⋊#15668589 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8757, 9);