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C22⋊C4×C4⋊AGL(1,𝔽5) #13027996

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC22⋊C4×C4⋊AGL(1,𝔽5)

Splittings

FittingC4×C5×C22⋊C4 ⋊ C4
SylowC5 ⋊ C22⋊C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC4×C5×C22⋊C4C4
socleC23×C5C23×C4
prime radicalC24×D5C23
cosocleC23×D5C24
hypercenterC4×C22⋊C4AGL(1,𝔽5)
hypocenterC5C22⋊C4×C4⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1098264);