Finite Group Databasebeta

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C19⋊C3×D165 #34037890

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

Aliases

direct productC19⋊C3×D165
unambiguous semidirect productC3⋊(C19⋊C3×D55)
unambiguous semidirect productC5⋊(C19⋊C3×D33)
unambiguous semidirect productC11⋊(D15×C19⋊C3)
unambiguous semidirect product(C19×D165)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C19 ⋊ C2×C3
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallC3×C11×C19⋊C3 ⋊ D5
HallC5×C11×C19 ⋊ C3×D3
HallC3×C5×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C3×D15
HallC3×C19⋊C3 ⋊ D55
HallC5×C19 ⋊ C3×D33
HallC5×C11 ⋊ D3×C19⋊C3
SylowC19 ⋊ C3×D165
SylowC11 ⋊ D15×C19⋊C3
SylowC5 ⋊ C19⋊C3×D33

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD19⋊C3×D165, (C11⋊(D19⋊C3))⋊D15, D11×D15×C19⋊C3, …
maximal normal subgroup ofD19⋊C3×D165, (C11⋊(D19⋊C3))⋊D15, D11×D15×C19⋊C3, …
maximal quotient ofC19⋊C3×Dic165, C2×C19⋊C3×D165

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 83);