Finite Group Databasebeta

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C2×#10598713 #13014615

order1280
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10598713

Splittings

SylowC5 ⋊ C2×#1271

Subgroups

subgroupG/H
centerC24C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socle, prime radicalC24×C5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×#1271
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1084883);