Finite Group DatabasebetaFinite Group Databasebeta| order | 22743 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C361 ⋊ C9 |
| Sylow | C361 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #15692423 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #21439055 |
| commutator, hypocenter | C7×C361 | C9 |
| Frattini | C3×C19 | #87704 |
| Fitting, cosocle | C3×C7×C361 | C3 |
| socle, prime radical | C3×C7×C19 | C19⋊C3 |
| LCS | G ▷ C7×C361 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22743 |
Polycyclic presentation:
3,7,19,3,19|a^3=d,c^19=e^14,b^a=b^2,c^a=c^7e,e^a=e^72535 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22743, 4);