Finite Group Databasebeta

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C5×C11×C3⋊(D19⋊C3) #34037883

order18810
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C3⋊(D19⋊C3)
unambiguous semidirect productC3⋊(C5×C11×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C5×D3×C11)
unambiguous semidirect productD57⋊(C3×C5×C11)
unambiguous semidirect product(C5×D57)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D57)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C3
derivedC3×C19 ⋊ C2×C3×C5×C11
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC5×C11×C19 ⋊ C3×D3
HallC3×C5×C19⋊C3 ⋊ C2×C11
HallC11×C19 ⋊ C3×C5×D3
HallC3×C19⋊C3 ⋊ C2×C5×C11
HallC5×C19 ⋊ C3×D3×C11
SylowC19 ⋊ C3×C5×D3×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊(D19⋊C3)
commutator, cosocle, hypocenterC3×C19C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C3
LCSG ▷ C3×C19
UCSC1 ◁ C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D3×C11×D19⋊C3, C5×D11×C3⋊(D19⋊C3), C5×D33⋊(D19⋊C3), …
maximal normal subgroup ofC5×D3×C11×D19⋊C3, C5×D11×C3⋊(D19⋊C3), C5×D33⋊(D19⋊C3), …
maximal quotient ofC5×C11×C3⋊((C19⋊C3)⋊C4), C2×C5×C11×C3⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 76);