Finite Group Databasebeta

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C2×D5×#453 #12965899

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×D5×#453

Splittings

FittingC2×C5×#453 ⋊ C2
SylowC5 ⋊ C22×#453

Subgroups

subgroupG/H
centerC22D5×#120
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#453C2
socleC22×C5C2×#120
hypercenterC2×#453D5
hypocenterC5C22×#453
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

5670 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 ofC2×C5⋊D5×#453, C2×#72213351, C2×AGL(1,𝔽5)×#453, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#453, D5×#61110, #72221508, …
maximal quotient ofC2×C5⋊D5×#453, C2×#72213351, D3×D5×#453

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1036167);