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C3×C43⋊AGL(1,𝔽11) #28382005

order14190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C43⋊AGL(1,𝔽11)
unambiguous semidirect product(C11⋊C5)⋊(C3×D43)
unambiguous semidirect product(C3×D473)⋊C5

Splittings

Fitting, socle, HallC3×C11×C43 ⋊ C2×C5
derived, HallC11×C43 ⋊ C2×C3×C5
HallC3×C43×C11⋊C5 ⋊ C2
HallC3×D473 ⋊ C5
HallC43×C11⋊C5 ⋊ C2×C3
HallD473 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ D43
HallC3×C43 ⋊ AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D43
SylowC43 ⋊ C3×AGL(1,𝔽11)
HallC3×C11 ⋊ C5×D43
SylowC11 ⋊ C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC3C43⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC11×C43C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C43C2×C5
LCSG ▷ C11×C43
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1419

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D43×AGL(1,𝔽11), D3×C43⋊AGL(1,𝔽11), D129⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×D43×AGL(1,𝔽11), D3×C43⋊AGL(1,𝔽11), D129⋊AGL(1,𝔽11), …
maximal quotient ofC3×C43⋊(Dic11⋊C5), C2×C3×C43⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 22);