Finite Group DatabasebetaFinite Group Databasebeta| order | 22068 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C613 ⋊ C4×C9 |
| Hall | #19149452 ⋊ C4 |
| Hall | #14578580 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C613 | C4×C9 |
| prime radical, cosocle | D613⋊C3 | C2×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 613 |
Polycyclic presentation:
2,3,2,3,613|a^2=c,b^3=d,e^a=e^578,e^b=e^592,e^c=e^612,e^d=e^54753 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22068, 32);