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C2×#10605017 #13034189

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#10605017
unambiguous semidirect productD5⋊#1790

Splittings

FittingC2×C5×H(5,𝔽2) ⋊ C4
SylowC5 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC22#65800
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C5×H(5,𝔽2)C4
socleC22×C5#379
prime radicalC2×D5×H(5,𝔽2)C2
cosocleC23×D5C24
hypercenterC2×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C2×#1790
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×H(5,𝔽2)

4402 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×AGL(1,𝔽5)×B(4,𝔽2), D3×#10605017, AGL(1,𝔽5)×#1790, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×B(4,𝔽2), AGL(1,𝔽5)×#1790, #72242721, …
maximal quotient of#72221422, #72221463, D3×#10605017, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104457);