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AGL(1,𝔽5)×H(3,ℤ/4) #13021570

order1280
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productAGL(1,𝔽5)×H(3,ℤ/4)

Splittings

FittingC5×H(3,ℤ/4) ⋊ C4
SylowC5 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC4C42×AGL(1,𝔽5)
commutatorC4×C5C43
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×H(3,ℤ/4)C4
socleC2×C5C4×#95
prime radicalC23×D5C2×D4
cosocleC22×C4×D5C23
hypercenterH(3,ℤ/4)AGL(1,𝔽5)
hypocenterC5C4×H(3,ℤ/4)
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C4 ◁ H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2010, AGL(1,𝔽5)×#1904, AGL(1,𝔽5)×#1910, …
maximal normal subgroup ofAGL(1,𝔽5)×#2010, AGL(1,𝔽5)×#1904, AGL(1,𝔽5)×#1910, …
maximal quotient of#72221594, #72226418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1091838);