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C3×C11⋊C5×D57 #34037870

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

Aliases

direct productC3×C11⋊C5×D57
unambiguous semidirect productC3⋊(C3×D19×C11⋊C5)
unambiguous semidirect product(C3×C11×D57)⋊C5

Splittings

Fitting, socle, HallC32×C11×C19 ⋊ C2×C5
derivedC3×C11×C19 ⋊ C2×C3×C5
HallC32×C19×C11⋊C5 ⋊ C2
HallC3×C11×D57 ⋊ C5
HallC19×C11⋊C5 ⋊ C3×D3
HallC32×C11⋊C5 ⋊ D19
HallC11×C19 ⋊ C3×C5×D3
HallC32×C19 ⋊ C2×C11⋊C5
HallC32×C11 ⋊ C5×D19
SylowC19 ⋊ C3×D3×C11⋊C5
SylowC11 ⋊ C3×C5×D57
SylowC32 ⋊ D19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D57
commutator, cosocle, hypocenterC3×C11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC32×C11×C19C2×C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1254

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×AGL(1,𝔽11)×D57, C3×D57⋊AGL(1,𝔽11), C3×D3×D19×C11⋊C5, …
maximal normal subgroup ofC3×AGL(1,𝔽11)×D57, C3×D57⋊AGL(1,𝔽11), C3×D3×D19×C11⋊C5, …
maximal quotient ofC3×C11⋊C5×Dic57, C2×C3×C11⋊C5×D57

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 63);