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C3×C5⋊((C11⋊C5)⋊D11) #31827641

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

Aliases

direct productC3×C5⋊((C11⋊C5)⋊D11)
unambiguous semidirect productC5⋊(C3×(C11⋊C5)⋊D11)
unambiguous semidirect product(C11⋊C5)⋊(C3×D55)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3C5⋊((C11⋊C5)⋊D11)
commutator, cosocle, hypocenterC5×C112C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C5×C112
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 825

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D5×(C11⋊C5)⋊D11, C3×D11×C5⋊AGL(1,𝔽11), C3×AGL(1,𝔽11)×D55, …
maximal normal subgroup ofC3×D5×(C11⋊C5)⋊D11, C3×D11×C5⋊AGL(1,𝔽11), C3×AGL(1,𝔽11)×D55, …
maximal quotient ofC3×(C11⋊C5)⋊Dic55, C2×C3×C5⋊((C11⋊C5)⋊D11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 125);