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C5×C3⋊((C11⋊C5)⋊D11) #31827656

order18150
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C3⋊((C11⋊C5)⋊D11)
unambiguous semidirect productC3⋊(C5×(C11⋊C5)⋊D11)
unambiguous semidirect product(C11⋊C5)⋊(C5×D33)

Splittings

Fitting, socleC3×C5×C112 ⋊ C2×C5
derived, HallC3×C112 ⋊ C2×C52
HallC3×C5×C11×C11⋊C5 ⋊ C2
HallC5×C11×C11⋊C5 ⋊ D3
HallC3⋊(C11⋊D11) ⋊ C52
SylowC112 ⋊ C52×D3
SylowC3 ⋊ C5×(C11⋊C5)⋊D11

Subgroups

subgroupG/H
center, hypercenterC5C3⋊((C11⋊C5)⋊D11)
commutator, cosocle, hypocenterC3×C112C2×C52
FrattiniC1G
Fitting, socleC3×C5×C112C2×C5
LCSG ▷ C3×C112
UCSC1 ◁ C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 825

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D3×(C11⋊C5)⋊D11, C5×D11×C3⋊AGL(1,𝔽11), C5×D33×AGL(1,𝔽11), …
maximal normal subgroup ofC5×D3×(C11⋊C5)⋊D11, C5×D11×C3⋊AGL(1,𝔽11), C5×D33×AGL(1,𝔽11), …
maximal quotient ofC5×C3⋊((C11⋊C5)⋊Dic11), C2×C5×C3⋊((C11⋊C5)⋊D11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 140);