Finite Group Databasebeta

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C3⋊D3×C19×C11⋊C5 #34037873

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC3⋊D3×C19×C11⋊C5
unambiguous semidirect productC3⋊(D3×C19×C11⋊C5)
unambiguous semidirect product(C11×C3⋊D3)⋊(C5×C19)
unambiguous semidirect product(C11×C3⋊D3×C19)⋊C5

Splittings

Fitting, socle, HallC32×C11×C19 ⋊ C2×C5
derived, HallC32×C11 ⋊ C2×C5×C19
HallC32×C19×C11⋊C5 ⋊ C2
HallC11×C3⋊D3×C19 ⋊ C5
HallC32×C11⋊C5 ⋊ C2×C19
HallC11×C19 ⋊ C5×C3⋊D3
HallC11×C3⋊D3 ⋊ C5×C19
HallC32×C19 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×C3⋊D3×C19
SylowC32 ⋊ C2×C19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC19C3⋊D3×C11⋊C5
commutator, cosocle, hypocenterC32×C11C2×C5×C19
FrattiniC1G
Fitting, socleC32×C11×C19C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1881

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC19×(C11⋊C5)⋊#157, C19⋊((C11⋊C5)⋊#157), C19×#157×C11⋊C5, …
maximal normal subgroup ofC19×(C11⋊C5)⋊#157, C19⋊((C11⋊C5)⋊#157), C19×#157×C11⋊C5, …
maximal quotient ofC19×C3⋊Dic3×C11⋊C5, C2×C3⋊D3×C19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 66);