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C5×D11×AGL(1,𝔽11) #27130887

order12100
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×D11×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C52×D11)

Splittings

Fitting, socleC5×C112 ⋊ C22×C5
derived, SylowC112 ⋊ C22×C52
HallC5×C11×C11⋊C5 ⋊ C22
HallD112 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5D11×AGL(1,𝔽11)
commutator, cosocle, hypocenterC112C22×C52
FrattiniC1G
Fitting, socleC5×C112C22×C5
LCSG ▷ C112
UCSC1 ◁ C5

164 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

385 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D11×AGL(1,𝔽11), C5×D11×C3⋊AGL(1,𝔽11), C5×D33×AGL(1,𝔽11), …
maximal normal subgroup ofC3×C5×D11×AGL(1,𝔽11)
maximal quotient ofC3×C5×D11×AGL(1,𝔽11), C5×D11×C3⋊AGL(1,𝔽11), C5×D33×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 166);