Finite Group Databasebeta

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C2×C3×C11×C3⋊AGL(1,𝔽11) #36345232

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

Aliases

direct productC2×C3×C11×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C3×C11×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D3×C11)
unambiguous semidirect product(C2×D33)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C3×D33)⋊(C5×C11)

Splittings

Fitting, socleC2×C32×C112 ⋊ C2×C5
derivedC3×C11 ⋊ C22×C3×C5×C11
HallC32×C11×C11⋊C5 ⋊ C22
HallC2×C3×C11×D33 ⋊ C5
HallC32×C112 ⋊ C22×C5
HallC11×C11⋊C5 ⋊ C2×C3×D3
SylowC112 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×C11×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C112C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C11

188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 581);