Finite Group DatabasebetaFinite Group Databasebeta| order | 7810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C71 ⋊ C2×C5 |
| Hall | #16840848 ⋊ C2 |
| Hall | D11×C71 ⋊ C5 |
| Sylow | C71 ⋊ AGL(1,𝔽11) |
| Hall | D11 ⋊ C71⋊C5 |
| Sylow | C11 ⋊ C2×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C71 | C2×C5 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,71|c^a=c^10,c^b=c^4,d^b=d^54109 conjugacy classes — view the full character table.
| maximal subgroup of | #21462835⋊C2, C2×#21462841, C3×#21462841, … |
| maximal normal subgroup of | #21462835⋊C2, C2×#21462841, C3×#21462841 |
| maximal quotient of | #30626790, C2×#21462841, C3×#21462841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7810, 23);