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AGL(1,𝔽5)×PSU(3,𝔽2) #13089543

order1440
isoclinismisoclinic class of AGL(1,𝔽5)×PSU(3,𝔽2)
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productAGL(1,𝔽5)×PSU(3,𝔽2)

Splittings

Fitting, socle, HallC32×C5 ⋊ C4×Q8
SylowC32 ⋊ Q8×AGL(1,𝔽5)
SylowC5 ⋊ C4×PSU(3,𝔽2)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutatorC5×C3⋊D3C22×C4
Fitting, socle, hypocenterC32×C5C4×Q8
prime radical, cosocleD5×C3⋊D3C23
LCSG ▷ C5×C3⋊D3 ▷ C32×C5
UCSC1

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 45

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×PSU(3,𝔽2)⋊C3, AGL(1,𝔽5)×AΓL(1,𝔽9), C3×AGL(1,𝔽5)×PSU(3,𝔽2), …
maximal normal subgroup ofAGL(1,𝔽5)×PSU(3,𝔽2)⋊C3, AGL(1,𝔽5)×AΓL(1,𝔽9), C3×AGL(1,𝔽5)×PSU(3,𝔽2), …
maximal quotient ofC3×AGL(1,𝔽5)×PSU(3,𝔽2), C2×AGL(1,𝔽5)×PSU(3,𝔽2)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5860);