Finite Group DatabasebetaFinite Group Databasebeta| order | 22068 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic613⋊C3 |
| unambiguous semidirect product | Dic613⋊C32 |
| unambiguous semidirect product | (C3×Dic613)⋊C3 |
| derived, Sylow | C613 ⋊ C32×C4 |
| Hall | C3×C613⋊C3 ⋊ C4 |
| Hall | Dic613 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D613⋊C3 |
| commutator, hypocenter | C613 | C32×C4 |
| Frattini | C2 | C3×D613⋊C3 |
| Fitting, socle | C2×C3×C613 | C2×C3 |
| prime radical | C2×C3×C613⋊C3 | C2 |
| cosocle | C2×C613 | C2×C32 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7356 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22068, 22);