Finite Group Databasebeta

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C22×#65758 #13044502

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

Aliases

direct productC22×#65758

Splittings

SylowC5 ⋊ C22×#423

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC24×C4×C5C4
socleC24×C5C22×C4
prime radicalC25×C5C2×C4
cosocleC2×Dic5C25
hypercenterC24×C4AGL(1,𝔽5)
hypocenterC5C22×#423
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C24×C4

3438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

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, 1114770);