Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C1849⋊C3)⋊C4 |
| unambiguous semidirect product | Dic1849⋊C3 |
| derived, Sylow | C1849 ⋊ C3×C4 |
| Hall | Dic1849 ⋊ C3 |
| Hall | C1849⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1849⋊C3 |
| commutator, hypocenter | C1849 | C3×C4 |
| Frattini, socle | C2×C43 | D43⋊C3 |
| Fitting, cosocle | C2×C1849 | C2×C3 |
| prime radical | C2×C1849⋊C3 | C2 |
| LCS | G ▷ C1849 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7396 |
Polycyclic presentation:
2,3,43,2,43|a^2=d,c^43=e^42,c^a=c^42e,e^a=e^42,c^b=c^36e^34,e^b=e^36628 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 2);