Finite Group Databasebeta

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C2×C5×C22⋊H(3,𝔽3) #11761998

order1080
isoclinismisoclinic class of C9⋊A4
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×C5×C22⋊H(3,𝔽3)
unambiguous semidirect productC23⋊(C5×H(3,𝔽3))
unambiguous semidirect product(C2×C32)⋊(C5×A4)
unambiguous semidirect product(C23×C5)⋊H(3,𝔽3)
unambiguous semidirect product(C2×C3×A4)⋊(C3×C5)
unambiguous semidirect product(C2×C32×C5)⋊A4
unambiguous semidirect product(C2×C3×C5×A4)⋊C3

Splittings

FittingC23×C32×C5 ⋊ C3
HallC23×C5 ⋊ H(3,𝔽3)
SylowC23 ⋊ C5×H(3,𝔽3)

Subgroups

subgroupG/H
centerC2×C3×C5C3×A4
commutator, cosocleC22×C3C2×C32×C5
FrattiniC3C2×C3×C5×A4
FittingC23×C32×C5C3
socleC23×C3×C5C32
hypercenterC2×C32×C5A4
hypocenterC22C2×C5×H(3,𝔽3)
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3×C5 ◁ C2×C32×C5

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 90

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 344);