Finite Group DatabasebetaFinite Group Databasebeta| order | 9020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C11×C41 ⋊ C4×C5 |
| Hall | #14555918 ⋊ C4 |
| Hall | Dic451 ⋊ C5 |
| Sylow | C41 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ Dic41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #17985249 |
| commutator, hypocenter | C11×C41 | C4×C5 |
| Fitting, socle | C2×C11×C41 | C2×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,41,2|a^2=e,c^a=c^10,d^a=d^40,c^b=c^4,d^b=d^16110 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#22583160, C3⋊#22583160 |
| maximal normal subgroup of | C3×#22583160 |
| maximal quotient of | C3×#22583160, C3⋊#22583160 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9020, 31);