Finite Group DatabasebetaFinite Group Databasebeta| order | 22446 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | D3×C29×C43⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C29×C43⋊C3) |
| unambiguous semidirect product | (D3×C43)⋊(C3×C29) |
| unambiguous semidirect product | (D3×C29×C43)⋊C3 |
| Fitting, socle | C3×C29×C43 ⋊ C2×C3 |
| derived | C3×C43 ⋊ C2×C3×C29 |
| Hall | C3×C29×C43⋊C3 ⋊ C2 |
| Hall | C29×C43 ⋊ C3×D3 |
| Hall | C3×C43⋊C3 ⋊ C2×C29 |
| Sylow | C43 ⋊ C3×D3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D3×C43⋊C3 |
| commutator, cosocle, hypocenter | C3×C43 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C43 | C2×C3 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C29 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3741 |
1479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22446, 18);