Finite Group DatabasebetaFinite Group Databasebeta| order | 22068 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C613 ⋊ C4×C9 |
| Hall | #19149452 ⋊ C4 |
| Hall | Dic613 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19149452⋊C2 |
| commutator, hypocenter | C613 | C4×C9 |
| Fitting, socle | C2×C613 | C2×C9 |
| prime radical, cosocle | C2×C613⋊C3 | C2×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2452 |
Polycyclic presentation:
2,3^2,613,2|a^2=e,b^3=c,d^a=d^612,d^b=d^592,d^c=d^547104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22068, 20);