Finite Group Databasebeta

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C2×C32×C11×AGL(1,𝔽11) #36345220

order21780
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C11×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C32×C5×C11)
unambiguous semidirect product(C2×D11)⋊(C32×C5×C11)
unambiguous semidirect product(C11⋊C5)⋊(C22×C32×C11)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C32×C11)
unambiguous semidirect product(C2×C3×D11)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C32×D11)⋊(C5×C11)

Splittings

Fitting, socleC2×C32×C112 ⋊ C2×C5
derivedC11 ⋊ C22×C32×C5×C11
HallC32×C11×C11⋊C5 ⋊ C22
HallC2×C32×C11×D11 ⋊ C5
HallC32×C112 ⋊ C22×C5
HallC11×C11⋊C5 ⋊ C22×C32
HallC2×C11×D11 ⋊ C32×C5
SylowC112 ⋊ C22×C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C112C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C32×C11

252 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 569);