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C2×D5⋊#446 #13044790

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×D5⋊#446
unambiguous semidirect productD5⋊(C2×#446)

Splittings

SylowC5 ⋊ C22×#446

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC2×Dic5C25
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5C22×#446
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

2222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1115058);