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C22×C3×A5 #10624303

order720
isoclinismisoclinic class of A5
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C22

Aliases

direct productC22×C3×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC22×C3A5
commutator, hypocenterA5C22×C3
FrattiniC1G
LCSG ▷ A5
UCSC1 ◁ C22×C3

157 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 60

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

derived subgroup ofD3×A4×A5
socle ofC2×C3×A5⋊C4, C2×C3⋊(A5⋊C4), C2×Dic3×A5, …
maximal subgroup ofC2×C3×A5⋊C4, C3×C22⋊S5, C2×C3⋊(A5⋊C4), …
maximal normal subgroup ofC2×C3×A5⋊C4, C3×C22⋊S5, C2×C3⋊(A5⋊C4), …
maximal quotient ofC2×C3×C4×A5, C2×C3×#6732, C3×D4×A5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 772);