Finite Group DatabasebetaFinite Group Databasebeta| order | 11186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D799 |
| unambiguous semidirect product | C17⋊(C7×D47) |
| unambiguous semidirect product | C47⋊(C7×D17) |
| Fitting, socle, Hall | C7×C17×C47 ⋊ C2 |
| derived, Hall | C17×C47 ⋊ C2×C7 |
| Hall | C7×C47 ⋊ D17 |
| Hall | C7×C17 ⋊ D47 |
| Sylow | C47 ⋊ C7×D17 |
| Sylow | C17 ⋊ C7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D799 |
| commutator, cosocle, hypocenter | C17×C47 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C47 | C2 |
| LCS | G ▷ C17×C47 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
2807 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D17×D47, D7×D799, D119⋊D47, … |
| maximal normal subgroup of | C7×D17×D47, D7×D799, D119⋊D47, … |
| maximal quotient of | C7×Dic799, C2×C7×D799, C3×C7×D799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11186, 4);