Finite Group DatabasebetaFinite Group Databasebeta| order | 22068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#19149450⋊C2 |
| unambiguous semidirect product | #19149450⋊C22 |
| unambiguous semidirect product | (C2×#19149450)⋊C2 |
| derived, Sylow | C613 ⋊ C22×C9 |
| Hall | #19149450 ⋊ C22 |
| Hall | C2×D613 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D613⋊C3 |
| commutator, hypocenter | C613 | C22×C9 |
| Frattini | C3 | C2×D613⋊C3 |
| Fitting, socle | C2×C3×C613 | C2×C3 |
| prime radical | C2×C3×D613 | C3 |
| cosocle | C3×C613 | C22×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11034 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22068, 9);