Finite Group Databasebeta

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C3×C19⋊C3×D55 #34037882

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

Aliases

direct productC3×C19⋊C3×D55
unambiguous semidirect productC5⋊(C3×D11×C19⋊C3)
unambiguous semidirect productC11⋊(C3×D5×C19⋊C3)
unambiguous semidirect product(C19×D55)⋊C32
unambiguous semidirect product(C3×C19×D55)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C3
derived, HallC5×C11×C19 ⋊ C2×C32
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallC19×D55 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ D5
HallC3×C5×C19⋊C3 ⋊ D11
HallC11×C19 ⋊ C32×D5
HallC5×C19 ⋊ C32×D11
HallC5×C11 ⋊ C2×C3×C19⋊C3
SylowC19 ⋊ C32×D55
SylowC11 ⋊ C3×D5×C19⋊C3
SylowC5 ⋊ C3×D11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C19⋊C3×D55
commutator, cosocle, hypocenterC5×C11×C19C2×C32
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D55×D19⋊C3, C3×D55⋊(D19⋊C3), C3×D5×D11×C19⋊C3, …
maximal normal subgroup ofC3×D55×D19⋊C3, C3×D55⋊(D19⋊C3), C3×D5×D11×C19⋊C3, …
maximal quotient ofC3×C19⋊C3×Dic55, C2×C3×C19⋊C3×D55

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 75);