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C11×PSL(2,𝔽11) #20300134

order7260
isoclinismisoclinic class of PSL(2,𝔽11)
automorphism?
homologyAbelianization (H1) = C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×PSL(2,𝔽11)

Subgroups

subgroupG/H
center, Fitting, hypercenterC11PSL(2,𝔽11)
commutator, hypocenterPSL(2,𝔽11)C11
FrattiniC1G
LCSG ▷ PSL(2,𝔽11)
UCSC1 ◁ C11

34 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC11⋊C5×PSL(2,𝔽11)
socle ofC11⋊C5×PSL(2,𝔽11)
maximal subgroup ofC3×C11×PSL(2,𝔽11), C5×C11×PSL(2,𝔽11), C11⋊C5×PSL(2,𝔽11)
maximal normal subgroup ofC3×C11×PSL(2,𝔽11), C5×C11×PSL(2,𝔽11), C11⋊C5×PSL(2,𝔽11)
maximal quotient ofC3×C11×PSL(2,𝔽11), C5×C11×PSL(2,𝔽11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 234);