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C3×C11×C5⋊AGL(1,𝔽11) #31827632

order18150
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C5⋊AGL(1,𝔽11)
unambiguous semidirect productC5⋊(C3×C11×AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3×D5×C11)
unambiguous semidirect productD55⋊(C3×C5×C11)
unambiguous semidirect product(C3×D55)⋊(C5×C11)

Splittings

Fitting, socleC3×C5×C112 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C3×C5×C11
HallC3×C5×C11×C11⋊C5 ⋊ C2
HallC5×C11×C11⋊C5 ⋊ C2×C3
HallC3×C112 ⋊ C5×D5
SylowC112 ⋊ C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC3×C11C5⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3×C11

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D5×C11×AGL(1,𝔽11), C3×D11×C5⋊AGL(1,𝔽11), C3×(C5⋊AGL(1,𝔽11))⋊D11, …
maximal normal subgroup ofC3×D5×C11×AGL(1,𝔽11), C3×D11×C5⋊AGL(1,𝔽11), C3×(C5⋊AGL(1,𝔽11))⋊D11, …
maximal quotient ofC3×C11×(C11⋊C5)⋊Dic5, C2×C3×C11×C5⋊AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 116);