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C5×A6 #14268361

order1800
isoclinismisoclinic class of A6
automorphism?
homologyAbelianization (H1) = C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC5×A6

Subgroups

subgroupG/H
center, Fitting, hypercenterC5A6
commutator, hypocenterA6C5
FrattiniC1G
LCSG ▷ A6
UCSC1 ◁ C5

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

derived subgroup ofDic5×A6
maximal subgroup ofD5×A6, C5×PGL(2,𝔽9), C2×C5×A6
maximal normal subgroup ofD5×A6, C5×PGL(2,𝔽9), C2×C5×A6
maximal quotient ofC5×SL(2,𝔽9), C2×C5×A6, C5×#11761914

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 555);