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C5×C22⋊H(3,𝔽3) #10587401

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

Aliases

direct productC5×C22⋊H(3,𝔽3)
unambiguous semidirect productC22⋊(C5×H(3,𝔽3))
unambiguous semidirect productC32⋊(C5×A4)
unambiguous semidirect product(C22×C5)⋊H(3,𝔽3)
unambiguous semidirect product(C3×A4)⋊(C3×C5)
unambiguous semidirect product(C32×C5)⋊A4
unambiguous semidirect product(C3×C5×A4)⋊C3

Splittings

FittingC22×C32×C5 ⋊ C3
HallC22×C5 ⋊ H(3,𝔽3)
SylowC22 ⋊ C5×H(3,𝔽3)

Subgroups

subgroupG/H
centerC3×C5C3×A4
commutator, cosocleC22×C3C32×C5
FrattiniC3C3×C5×A4
FittingC22×C32×C5C3
socleC22×C3×C5C32
hypercenterC32×C5A4
hypocenterC22C5×H(3,𝔽3)
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C3×C5 ◁ C32×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC5⋊#6258
maximal subgroup ofC5×(C3⋊S4)⋊C3, C5⋊((C3⋊S4)⋊C3), C5×#6258, …
maximal normal subgroup ofC5×(C3⋊S4)⋊C3, C5⋊((C3⋊S4)⋊C3), C5×#6258, …
maximal quotient ofC5×Q8⋊H(3,𝔽3), C2×C5×C22⋊H(3,𝔽3), C5×#66357, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 61);