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C7×C29×A5 #27131830

order12180
isoclinismisoclinic class of A5
automorphism?
homologyAbelianization (H1) = C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC7×C29×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC7×C29A5
commutator, hypocenterA5C7×C29
FrattiniC1G
LCSG ▷ A5
UCSC1 ◁ C7×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1015 conjugacy classes. The character table is too large to display.

Relationships

socle ofΓL(1,𝔽8)×C29×A5
maximal subgroup ofC3×C7×C29×A5, ΓL(1,𝔽8)×C29×A5
maximal normal subgroup ofC3×C7×C29×A5, ΓL(1,𝔽8)×C29×A5
maximal quotient ofC3×C7×C29×A5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 165);