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C2×#10604461 #13034961

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

Aliases

direct productC2×#10604461
unambiguous semidirect productD5⋊#1889

Splittings

FittingC2×C5×#120 ⋊ C4
SylowC5 ⋊ C2×#1889

Subgroups

subgroupG/H
centerC22#65779
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C5×#120C4
socleC22×C5#386
prime radicalC2×D5×#120C2
cosocleC23×D5C24
hypercenterC2×#120AGL(1,𝔽5)
hypocenterC5C2×#1889
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×#120

3566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221422, #72221463, C2×AGL(1,𝔽5)×B(4,𝔽2), …
maximal normal subgroup of#72221422, #72221463, C2×AGL(1,𝔽5)×B(4,𝔽2), …
maximal quotient ofD3×#10604461, #72242752, #72242753, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105229);