Finite Group Databasebeta

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C2×#10604635 #13030743

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#10604635

Splittings

SylowC5 ⋊ C2×#1530

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC2×#66059C2
cosocleC4×Dic5C24
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C2×#1530
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

1330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1101011);