Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×C1849⋊C3 |
| unambiguous semidirect product | (C4×C1849)⋊C3 |
| Fitting, Hall | C4×C1849 ⋊ C3 |
| derived, Sylow | C1849 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C1849⋊C3 |
| commutator, hypocenter | C1849 | C3×C4 |
| Frattini, socle | C2×C43 | C2×C43⋊C3 |
| Fitting | C4×C1849 | C3 |
| prime radical | C2×C1849⋊C3 | C2 |
| cosocle | C2×C1849 | C2×C3 |
| LCS | G ▷ C1849 | |
| UCS | C1 ◁ C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7396 |
2476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 3);