Finite Group DatabasebetaFinite Group Databasebeta| order | 8757 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C139 ⋊ C9 |
| Sylow | C139 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C139⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15668588 |
| commutator, hypocenter | C7×C139 | C9 |
| Fitting, socle | C3×C7×C139 | C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,139,3|a^3=d,b^a=b^2,c^a=c^42981 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22576804, #31776103, #31776107, … |
| maximal normal subgroup of | C2×#22576804, #31776103, #31776107, … |
| maximal quotient of | C2×#22576804, C22⋊#22576804 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8757, 4);