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C22×C5×PSU(3,𝔽2) #13089605

order1440
isoclinismisoclinic class of PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25×C3

Aliases

direct productC22×C5×PSU(3,𝔽2)

Splittings

Fitting, socleC22×C32×C5 ⋊ Q8
HallC32×C5 ⋊ C22×Q8
SylowC32 ⋊ C22×C5×Q8

Subgroups

subgroupG/H
center, hypercenterC22×C5PSU(3,𝔽2)
commutator, cosocleC3⋊D3C24×C5
FrattiniC1G
Fitting, socleC22×C32×C5Q8
prime radicalC22×C5×C3⋊D3C22
hypocenterC32C22×C5×Q8
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C22×C5

344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C5×PSU(3,𝔽2)⋊C3, C22×C3×C5×PSU(3,𝔽2), C22×C5×AΓL(1,𝔽9), …
maximal normal subgroup ofC22×C5×PSU(3,𝔽2)⋊C3, C22×C3×C5×PSU(3,𝔽2), C22×C5×AΓL(1,𝔽9), …
maximal quotient ofC22×C3×C5×PSU(3,𝔽2), C2×C4×C5×PSU(3,𝔽2)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5922);