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C2×D5×B(4,𝔽2) #12966011

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC2×D5×B(4,𝔽2)

Splittings

FittingC2×C5×B(4,𝔽2) ⋊ C2
SylowC5 ⋊ C22×B(4,𝔽2)

Subgroups

subgroupG/H
centerC22D5×#120
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×B(4,𝔽2)C2
socleC22×C5C2×#120
hypercenterC2×B(4,𝔽2)D5
hypocenterC5C22×B(4,𝔽2)
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×B(4,𝔽2)

7014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#23900, C2×AGL(1,𝔽5)×B(4,𝔽2), D3×D5×B(4,𝔽2), …
maximal normal subgroup ofD5×#33551, D5×#23900, C2×AGL(1,𝔽5)×B(4,𝔽2), …
maximal quotient ofD5×#33551, D5×#23900, D3×D5×B(4,𝔽2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1036279);