Finite Group DatabasebetaFinite Group Databasebeta| order | 9020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C41 ⋊ C4×C5 |
| Hall | #14555918 ⋊ C4 |
| Hall | C11⋊#4223 ⋊ C5 |
| Sylow | C41 ⋊ Dic11⋊C5 |
| Sylow | C11 ⋊ #4223⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C41 | C4×C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,11,41|a^2=c,d^a=d^10,e^a=e^32,d^b=d^4,e^b=e^16,e^c=e^4044 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#22583166, C3⋊#22583166 |
| maximal normal subgroup of | C3×#22583166 |
| maximal quotient of | C3×#22583166, C3⋊#22583166 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9020, 37);