Finite Group DatabasebetaFinite Group Databasebeta| order | 10186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C463⋊C11 |
| unambiguous semidirect product | (C2×C463)⋊C11 |
| Fitting, socle, Hall | C2×C463 ⋊ C11 |
| derived, Sylow | C463 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C463⋊C11 |
| commutator, cosocle, hypocenter | C463 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C463 | C11 |
| LCS | G ▷ C463 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
106 conjugacy classes — view the full character table.
| maximal subgroup of | Dic463⋊C11, C4×C463⋊C11, C2×D463⋊C11, … |
| maximal normal subgroup of | Dic463⋊C11, C4×C463⋊C11, C2×D463⋊C11, … |
| maximal quotient of | C4×C463⋊C11, C22×C463⋊C11, C2×C3×C463⋊C11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10186, 2);