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C2×D5×#442 #12963341

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×D5×#442

Splittings

FittingC2×C5×#442 ⋊ C2
SylowC5 ⋊ C22×#442

Subgroups

subgroupG/H
centerC23C2×D4×D5
commutatorC4×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C5×#442C2
socleC23×C5C22×D4
prime radicalC22×D5×D8C2
cosocleC2×C4×C5C25
hypercenterC2×#442D5
hypocenterC5C22×#442
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#442, C2×D5×AGL(1,ℤ/16), C2×#13025910, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#442, C2×D5×AGL(1,ℤ/16), C2×#13025910, …
maximal quotient ofC2×D5×AGL(1,ℤ/16), C2×C5⋊D5×#442

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1033609);