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C2×#10617409 #13044529

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#10617409
unambiguous semidirect productD5⋊#2911

Splittings

FittingC22×C5×M16 ⋊ C4
SylowC5 ⋊ C2×#2911

Subgroups

subgroupG/H
centerC2×C4C2×C4⋊AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC22×C5C22×C4⋊C4
prime radicalC24×D5D4
cosocleC4×D5C25
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C2×#2911
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114797);