Finite Group Databasebeta

← Prev (#22547763) Next (#22547765) →

C7×C19×A5 #22547764

order7980
isoclinismisoclinic class of A5
automorphism?
homologyAbelianization (H1) = C7×C19 · Schur multiplier (H2) = C2

Aliases

direct productC7×C19×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC7×C19A5
commutator, hypocenterA5C7×C19
FrattiniC1G
LCSG ▷ A5
UCSC1 ◁ C7×C19

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

derived subgroup ofA5×#87704, A5×#87705
socle ofC19×ΓL(1,𝔽8)×A5, C7×C19⋊C3×A5, A5×#87704, …
maximal subgroup ofC3×C7×C19×A5, C19×ΓL(1,𝔽8)×A5, C7×C19⋊C3×A5, …
maximal normal subgroup ofC3×C7×C19×A5, C19×ΓL(1,𝔽8)×A5, C7×C19⋊C3×A5, …
maximal quotient ofC3×C7×C19×A5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 189);