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C2×D5⋊#423 #13044503

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

Aliases

direct productC2×D5⋊#423
unambiguous semidirect productD5⋊(C2×#423)

Splittings

SylowC5 ⋊ C22×#423

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C42×C5C4
socleC23×C5C23×C4
prime radicalC24×D5C2×C4
cosocleC2×Dic5C25
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5C22×#423
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42

3438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114771);