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C3×C5×C11⋊(D19⋊C3) #34037877

order18810
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C11⋊(D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C3×C5×D11)
unambiguous semidirect product(C5×D209)⋊C32
unambiguous semidirect product(C3×C5×D209)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C3
derived, HallC11×C19 ⋊ C2×C32×C5
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallC5×D209 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C2×C5
HallC5×C11×C19 ⋊ C2×C32
HallC3×C5×C19⋊C3 ⋊ D11
HallD209 ⋊ C32×C5
HallC3×C19⋊C3 ⋊ C5×D11
HallC5×C19 ⋊ C32×D11
HallC5×C11 ⋊ C3×D19⋊C3
SylowC19 ⋊ C32×C5×D11
SylowC11 ⋊ C3×C5×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊(D19⋊C3)
commutator, cosocle, hypocenterC11×C19C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C3
LCSG ▷ C11×C19
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C5×D11×D19⋊C3, C3×D5×C11⋊(D19⋊C3), C3×D55⋊(D19⋊C3), …
maximal normal subgroup ofC3×C5×D11×D19⋊C3, C3×D5×C11⋊(D19⋊C3), C3×D55⋊(D19⋊C3), …
maximal quotient ofC3×C5×C11⋊((C19⋊C3)⋊C4), C2×C3×C5×C11⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 70);