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C5×C9⋊A4 #10587398

order540
isoclinismisoclinic class of C9⋊A4
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C9⋊A4
unambiguous semidirect productC9⋊(C5×A4)
unambiguous semidirect product(C5×C9)⋊A4

Splittings

FittingC22×C5×C9 ⋊ C3
HallC22×C5 ⋊ 3−1+2
SylowC22 ⋊ C5×3−1+2

Subgroups

subgroupG/H
centerC3×C5C3×A4
commutator, cosocleC22×C3C32×C5
FrattiniC3C3×C5×A4
FittingC22×C5×C9C3
socleC22×C3×C5C32
prime radicalC3×C5×A4C3
hypercenterC5×C9A4
hypocenterC22C5×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C3×C5 ◁ C5×C9

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C9⋊A4, C5×D9⋊A4, C5⋊(D9⋊A4), …
maximal normal subgroup ofD5×C9⋊A4, C5×D9⋊A4, C5⋊(D9⋊A4), …
maximal quotient ofC5×C9⋊SL(2,𝔽3), C2×C5×C9⋊A4, C5×(C22⋊C9)⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 58);