Finite Group DatabasebetaFinite Group Databasebeta| order | 19071 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C163 ⋊ C9 |
| Sylow | C163 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #13091814 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C163 | C9 |
| prime radical, cosocle | C13×C163⋊C3 | C3 |
| LCS | G ▷ C13×C163 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2119 |
Polycyclic presentation:
3^2,13,163|a^3=b^2,c^a=c^3,d^a=d^133,d^b=d^104255 conjugacy classes — view the full character table.
| maximal subgroup of | #49185904, #49185906, #49185910, … |
| maximal normal subgroup of | #49185904, #49185906, #49185910, … |
| maximal quotient of | C2×#34040176 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19071, 9);