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C3×C3⋊(C19⋊AGL(1,𝔽11)) #34037868

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

Aliases

direct productC3×C3⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C3×C19⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D57)
unambiguous semidirect product(C3×D627)⋊C5

Splittings

Fitting, socle, HallC32×C11×C19 ⋊ C2×C5
derivedC3×C11×C19 ⋊ C2×C3×C5
HallC32×C19×C11⋊C5 ⋊ C2
HallC3×D627 ⋊ C5
HallC19×C11⋊C5 ⋊ C3×D3
HallC32×C11⋊C5 ⋊ D19
HallC11×C19 ⋊ C3×C5×D3
HallC32×C19 ⋊ AGL(1,𝔽11)
HallC32×C11 ⋊ C5×D19
HallC11⋊C5 ⋊ C3×D57
SylowC19 ⋊ C3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D57
SylowC32 ⋊ C19⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C19⋊AGL(1,𝔽11))
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

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

Relationships

maximal subgroup ofC3×D19×C3⋊AGL(1,𝔽11), C3×AGL(1,𝔽11)×D57, C3×D3×C19⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D19×C3⋊AGL(1,𝔽11), C3×AGL(1,𝔽11)×D57, C3×D3×C19⋊AGL(1,𝔽11), …
maximal quotient ofC3×C3⋊(C19⋊(Dic11⋊C5)), C2×C3×C3⋊(C19⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 61);