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C2×#10605015 #13034197

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

Aliases

direct productC2×#10605015
unambiguous semidirect productD5⋊#1792

Splittings

FittingC2×C5×H(5,𝔽2) ⋊ C4
SylowC5 ⋊ C2×#1792

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×D5×H(5,𝔽2)C2
cosocleC2×C4×D5C24
hypercenterC2×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C2×#1792
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

4114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72221208, C2×#72213446, C2×AGL(1,𝔽5)×#453, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#453, #72221478, AGL(1,𝔽5)×#1792, …
maximal quotient ofC2×#72221208, C2×#72213446, D3×#10605015, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104465);