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C11×C3⋊(C5⋊AGL(1,𝔽11)) #31827662

order18150
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect productC3⋊(C11×C5⋊AGL(1,𝔽11))
unambiguous semidirect productC5⋊(C11×C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C11×D15)
unambiguous semidirect productD165⋊(C5×C11)

Splittings

Fitting, socleC3×C5×C112 ⋊ C2×C5
derivedC3×C5×C11 ⋊ C2×C5×C11
HallC3×C5×C11×C11⋊C5 ⋊ C2
HallC5×C11×C11⋊C5 ⋊ D3
HallC3×C112 ⋊ C5×D5
SylowC112 ⋊ C5×D15
SylowC3 ⋊ C11×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C5⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C5×C11C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×D15×AGL(1,𝔽11), D11×C3⋊(C5⋊AGL(1,𝔽11)), ((C11⋊C5)⋊D11)⋊D15, …
maximal normal subgroup ofC11×D15×AGL(1,𝔽11), D11×C3⋊(C5⋊AGL(1,𝔽11)), ((C11⋊C5)⋊D11)⋊D15, …
maximal quotient ofC11×C3⋊((C11⋊C5)⋊Dic5), C2×C11×C3⋊(C5⋊AGL(1,𝔽11))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 146);