Finite Group Databasebeta

← Prev (#34037865) Next (#34037867) →

C32×D19×C11⋊C5 #34037866

order18810
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×D19×C11⋊C5
unambiguous semidirect product(C32×C11×D19)⋊C5

Splittings

Fitting, socle, HallC32×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C32×C5
HallC32×C19×C11⋊C5 ⋊ C2
HallC32×C11×D19 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C32
HallC11×D19 ⋊ C32×C5
HallC32×C19 ⋊ C2×C11⋊C5
HallC32×C11 ⋊ C5×D19
SylowC19 ⋊ C2×C32×C11⋊C5
SylowC11 ⋊ C32×C5×D19

Subgroups

subgroupG/H
center, hypercenterC32D19×C11⋊C5
commutator, cosocle, hypocenterC11×C19C2×C32×C5
FrattiniC1G
Fitting, socleC32×C11×C19C2×C5
LCSG ▷ C11×C19
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

693 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D19×AGL(1,𝔽11), C3×D19×C3⋊AGL(1,𝔽11), C3×D3×D19×C11⋊C5, …
maximal normal subgroup ofC32×D19×AGL(1,𝔽11), C3×D19×C3⋊AGL(1,𝔽11), C3×D3×D19×C11⋊C5, …
maximal quotient ofC32×C11⋊C5×Dic19, C2×C32×D19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 59);