Finite Group DatabasebetaFinite Group Databasebeta| order | 9291 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C163 ⋊ C3 |
| Sylow | C163 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C163⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C163 | C3 |
| LCS | G ▷ C19×C163 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,19,163|b^a=b^7,c^a=c^581035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22604695, #32915714, #32915718, … |
| maximal normal subgroup of | C2×#22604695, #32915714, #32915718, … |
| maximal quotient of | C2×#22604695, #42124100, C3×#22604695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9291, 3);