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C7×PSL(2,𝔽13) #21439809

order7644
isoclinismisoclinic class of PSL(2,𝔽13)
automorphism?
homologyAbelianization (H1) = C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×PSL(2,𝔽13)

Subgroups

subgroupG/H
center, Fitting, hypercenterC7PSL(2,𝔽13)
commutator, hypocenterPSL(2,𝔽13)C7
FrattiniC1G
LCSG ▷ PSL(2,𝔽13)
UCSC1 ◁ C7

35 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

derived subgroup ofΓL(1,𝔽8)×PSL(2,𝔽13)
socle ofΓL(1,𝔽8)×PSL(2,𝔽13), C7×PGL(2,𝔽13)
maximal subgroup ofC3×C7×PSL(2,𝔽13), ΓL(1,𝔽8)×PSL(2,𝔽13), C5×C7×PSL(2,𝔽13), …
maximal normal subgroup ofC3×C7×PSL(2,𝔽13), ΓL(1,𝔽8)×PSL(2,𝔽13), C5×C7×PSL(2,𝔽13), …
maximal quotient ofC3×C7×PSL(2,𝔽13), C5×C7×PSL(2,𝔽13), C7×Sp(2,𝔽13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 378);