Finite Group Databasebeta

← Prev (#34037830) Next (#34037832) →

C11⋊C5×D171 #34037831

order18810
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D171
unambiguous semidirect productC9⋊(D19×C11⋊C5)
unambiguous semidirect productC19⋊(D9×C11⋊C5)
unambiguous semidirect product(C11×D171)⋊C5

Splittings

Fitting, derived, HallC9×C11×C19 ⋊ C2×C5
HallC9×C19×C11⋊C5 ⋊ C2
HallC11×D171 ⋊ C5
HallC19×C11⋊C5 ⋊ D9
HallC9×C11⋊C5 ⋊ D19
HallC11×C19 ⋊ C5×D9
HallC9×C19 ⋊ C2×C11⋊C5
HallC9×C11 ⋊ C5×D19
SylowC19 ⋊ D9×C11⋊C5
SylowC11 ⋊ C5×D171
SylowC9 ⋊ D19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C11×C19C2×C5
FrattiniC3C11⋊C5×D57
socleC3×C11×C19C5×D3
LCSG ▷ C9×C11×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×D171, D171⋊AGL(1,𝔽11), D9×D19×C11⋊C5, …
maximal normal subgroup ofAGL(1,𝔽11)×D171, D171⋊AGL(1,𝔽11), D9×D19×C11⋊C5, …
maximal quotient ofC11⋊C5×Dic171, C2×C11⋊C5×D171

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 24);