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C22×C4⋊C4×AGL(1,𝔽5) #13043827

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4⋊C4×AGL(1,𝔽5)

Splittings

FittingC22×C5×C4⋊C4 ⋊ C4
SylowC5 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC24×C5C22×C4
prime radicalC24×D5C23
cosocleC22×D5C25
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C22×C4×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal quotient ofAGL(1,𝔽5)×#2912, #72253215

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114095);