Finite Group DatabasebetaFinite Group Databasebeta| order | 9291 |
| isoclinism | isoclinic class of C163⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C163⋊C3 |
| unambiguous semidirect product | C163⋊(C3×C19) |
| Fitting, socle, Hall | C19×C163 ⋊ C3 |
| derived, Sylow | C163 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C163⋊C3 |
| commutator, hypocenter | C163 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C163 | C3 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
1083 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×C163⋊C3, C19×D163⋊C3, D19×C163⋊C3, … |
| maximal normal subgroup of | C2×C19×C163⋊C3, C19×D163⋊C3, D19×C163⋊C3, … |
| maximal quotient of | C2×C19×C163⋊C3, C19×#13091812, C3×C19×C163⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9291, 2);