Finite Group DatabasebetaFinite Group Databasebeta| order | 19287 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2143 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2143 | C9 |
| prime radical, cosocle | C2143⋊C3 | C3 |
| LCS | G ▷ C2143 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2143 |
Polycyclic presentation:
3^2,2143|a^3=b,c^a=c^1017,c^b=c^1793247 conjugacy classes — view the full character table.
| maximal subgroup of | #34064334⋊C2, C2×#34064334 |
| maximal normal subgroup of | #34064334⋊C2, C2×#34064334 |
| maximal quotient of | C2×#34064334 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19287, 3);