Finite Group DatabasebetaFinite Group Databasebeta| order | 10186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D463⋊C11 |
| unambiguous semidirect product | (C463⋊C11)⋊C2 |
| Fitting, socle, derived, Sylow | C463 ⋊ C2×C11 |
| Hall | C463⋊C11 ⋊ C2 |
| Hall | D463 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C463 | C2×C11 |
| LCS | G ▷ C463 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,463|c^a=c^462,c^b=c^15843 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D463⋊C11, C3×D463⋊C11, C3⋊(D463⋊C11), … |
| maximal normal subgroup of | C2×D463⋊C11, C3×D463⋊C11, (D463⋊C3)⋊C11 |
| maximal quotient of | Dic463⋊C11, C2×D463⋊C11, C3×D463⋊C11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10186, 1);