Finite Group Databasebeta

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D3×C11⋊C5×C19⋊C3 #34037855

order18810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11⋊C5×C19⋊C3
unambiguous semidirect productC3⋊(C2×C11⋊C5×C19⋊C3)
unambiguous semidirect product(D3×C11)⋊(C5×C19⋊C3)
unambiguous semidirect product(D3×C19)⋊(C3×C11⋊C5)
unambiguous semidirect product(D3×C11×C19⋊C3)⋊C5
unambiguous semidirect product(D3×C19×C11⋊C5)⋊C3

Splittings

Fitting, socle, derivedC3×C11×C19 ⋊ C2×C3×C5
HallC3×C11⋊C5×C19⋊C3 ⋊ C2
HallD3×C11×C19⋊C3 ⋊ C5
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC19×C11⋊C5 ⋊ C3×D3
HallC11×C19 ⋊ C3×C5×D3
HallC3×C19⋊C3 ⋊ C2×C11⋊C5
SylowC19 ⋊ C3×D3×C11⋊C5
SylowC11 ⋊ C5×D3×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C19C2×C3×C5
LCSG ▷ C3×C11×C19
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 627

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×(C11⋊C5)⋊(D19⋊C3), D3×C19⋊C3×AGL(1,𝔽11), D3×C11⋊C5×D19⋊C3, …
maximal normal subgroup ofD3×(C11⋊C5)⋊(D19⋊C3), D3×C19⋊C3×AGL(1,𝔽11), D3×C11⋊C5×D19⋊C3, …
maximal quotient ofDic3×C11⋊C5×C19⋊C3, C2×D3×C11⋊C5×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 48);