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C5×PSL(2,𝔽11) #15693235

order3300
isoclinismisoclinic class of PSL(2,𝔽11)
automorphism?
homologyAbelianization (H1) = C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×PSL(2,𝔽11)

Subgroups

subgroupG/H
center, Fitting, hypercenterC5PSL(2,𝔽11)
commutator, hypocenterPSL(2,𝔽11)C5
FrattiniC1G
LCSG ▷ PSL(2,𝔽11)
UCSC1 ◁ C5

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 55

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

derived subgroup ofD5×PSL(2,𝔽11)
socle ofD5×PSL(2,𝔽11)
maximal subgroup ofC5×C7×PSL(2,𝔽11), C5×C11×PSL(2,𝔽11), C11⋊C5×PSL(2,𝔽11), …
maximal normal subgroup ofC5×C7×PSL(2,𝔽11), C5×C11×PSL(2,𝔽11), C5×PGL(2,𝔽11), …
maximal quotient ofC5×C7×PSL(2,𝔽11), C5×C11×PSL(2,𝔽11), C11⋊C5×PSL(2,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 155);