Finite Group Databasebeta

← Prev (#13034202) Next (#13034204) →

C2×#10605016 #13034203

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#10605016

Splittings

FittingC2×C5×H(5,𝔽2) ⋊ C4
SylowC5 ⋊ C2×#1794

Subgroups

subgroupG/H
centerC22#65800
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×H(5,𝔽2)C4
socleC22×C5#379
prime radicalC2×#66285C2
cosocleC2×C4×D5C24
hypercenterC2×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C2×#1794
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

3662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104471);