Finite Group DatabasebetaFinite Group Databasebeta| order | 22055 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C401 ⋊ C5 |
| Sylow | C401 ⋊ C11⋊C5 |
| Sylow | C11 ⋊ C401⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C401 | C5 |
| LCS | G ▷ C11×C401 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4411 |
Polycyclic presentation:
5,11,401|b^a=b^3,c^a=c^39887 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22055, 3);