Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×(C43⋊C3)⋊C4 |
| unambiguous semidirect product | (C43⋊C3)⋊(C4×C43) |
| unambiguous semidirect product | Dic43⋊(C3×C43) |
| derived | C43 ⋊ C3×C4×C43 |
| Hall | C43×Dic43 ⋊ C3 |
| Hall | C43×C43⋊C3 ⋊ C4 |
| Sylow | C432 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D43⋊C3 |
| commutator, hypocenter | C43 | C3×C4×C43 |
| Frattini | C2 | C43×D43⋊C3 |
| Fitting, socle | C2×C432 | C2×C3 |
| prime radical | C2×C43×C43⋊C3 | C2 |
| cosocle | C2×C43 | C2×C3×C43 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C43 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 516 |
1118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 18);