Finite Group Databasebeta

← Prev (#34037862) Next (#34037864) →

C2×C3×C11⋊C5×C19⋊C3 #34037863

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

Aliases

direct productC2×C3×C11⋊C5×C19⋊C3
unambiguous semidirect product(C2×C11)⋊(C3×C5×C19⋊C3)
unambiguous semidirect product(C2×C19)⋊(C32×C11⋊C5)
unambiguous semidirect product(C2×C3×C11)⋊(C5×C19⋊C3)
unambiguous semidirect product(C2×C3×C19)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C11×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C19×C11⋊C5)⋊C32
unambiguous semidirect product(C2×C3×C11×C19⋊C3)⋊C5
unambiguous semidirect product(C2×C3×C19×C11⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C11×C19 ⋊ C3×C5
derived, HallC11×C19 ⋊ C2×C32×C5
HallC2×C3×C11×C19⋊C3 ⋊ C5
HallC2×C19×C11⋊C5 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C2×C32
HallC2×C11×C19 ⋊ C32×C5
HallC2×C19 ⋊ C32×C11⋊C5
HallC2×C11 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C2×C32×C11⋊C5
SylowC11 ⋊ C2×C3×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×C19⋊C3
commutator, cosocle, hypocenterC11×C19C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C19C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1254

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×(C11⋊C5)⋊((C19⋊C3)⋊C4), C3×C19⋊C3×Dic11⋊C5, C3×C11⋊C5×(C19⋊C3)⋊C4, …
maximal normal subgroup ofC3×(C11⋊C5)⋊((C19⋊C3)⋊C4), C3×C19⋊C3×Dic11⋊C5, C3×C11⋊C5×(C19⋊C3)⋊C4, …
maximal quotient ofC3×C4×C11⋊C5×C19⋊C3, C22×C3×C11⋊C5×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 56);