Finite Group DatabasebetaFinite Group Databasebeta| order | 19287 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C2143 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C2143⋊C3 |
| commutator, hypocenter | C2143 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C2143 | C3 |
| LCS | G ▷ C2143 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19287 |
Polycyclic presentation:
3^2,2143|a^3=b,c^a=c^17932151 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34064332⋊C2, C2×#34064332 |
| maximal normal subgroup of | #34064332⋊C2, C2×#34064332 |
| maximal quotient of | C2×#34064332 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19287, 1);