Finite Group Databasebeta

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C22×D5⋊#131 #13046028

order1280
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×D5⋊#131
unambiguous semidirect productD5⋊(C22×#131)

Splittings

SylowC5 ⋊ C23×#131

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C25×C4
FrattiniC2C25×AGL(1,𝔽5)
FittingC22×C5×#41C4
socleC23×C5C23×C4
prime radicalC22×D5×#41C2
cosocleDic5C26
hypercenterC22×#41AGL(1,𝔽5)
hypocenterC5C23×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×#41

11422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116296);