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C3×PSL(2,𝔽11) #14520432

order1980
isoclinismisoclinic class of PSL(2,𝔽11)
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×PSL(2,𝔽11)

Subgroups

subgroupG/H
center, Fitting, hypercenterC3PSL(2,𝔽11)
commutator, hypocenterPSL(2,𝔽11)C3
FrattiniC1G
LCSG ▷ PSL(2,𝔽11)
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

derived subgroup ofD3×PSL(2,𝔽11)
socle ofD3×PSL(2,𝔽11)
maximal subgroup ofC3×C7×PSL(2,𝔽11), ΓL(1,𝔽8)×PSL(2,𝔽11), C3×C11×PSL(2,𝔽11), …
maximal normal subgroup ofC3×C7×PSL(2,𝔽11), C3×C11×PSL(2,𝔽11), C3×C13×PSL(2,𝔽11), …
maximal quotient ofC3×C7×PSL(2,𝔽11), ΓL(1,𝔽8)×PSL(2,𝔽11), C3×C11×PSL(2,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 57);