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C32×C11×AGL(1,𝔽11) #24926140

order10890
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C32×C5×C11)
unambiguous semidirect product(C11⋊C5)⋊(C2×C32×C11)
unambiguous semidirect product(C3×D11)⋊(C3×C5×C11)
unambiguous semidirect product(C32×D11)⋊(C5×C11)

Splittings

Fitting, socle, HallC32×C112 ⋊ C2×C5
derivedC11 ⋊ C2×C32×C5×C11
HallC32×C11×C11⋊C5 ⋊ C2
HallC32×C11×D11 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×C32
HallC11×D11 ⋊ C32×C5
SylowC112 ⋊ C2×C32×C5

Subgroups

subgroupG/H
center, hypercenterC32×C11AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C2×C32×C5×C11
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C11
UCSC1 ◁ C32×C11

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1089 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D11×AGL(1,𝔽11), C3×D3×C11×AGL(1,𝔽11), C3×D33×AGL(1,𝔽11), …
maximal normal subgroup ofC32×D11×AGL(1,𝔽11), C3×D3×C11×AGL(1,𝔽11), C3×D33×AGL(1,𝔽11), …
maximal quotient ofC32×C11×Dic11⋊C5, C2×C32×C11×AGL(1,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 89);