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 | #19149450 ⋊ C4 |
| Hall | #14578580 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14578580⋊C3 |
| commutator, hypocenter | C613 | C4×C9 |
| Fitting, socle | C3×C613 | C3×C4 |
| prime radical, cosocle | C3×D613 | C2×C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5517 |
Polycyclic presentation:
2,3,2,613,3|a^2=c,b^3=e,d^a=d^578,d^b=d^547,d^c=d^612189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22068, 8);