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C2×#10604614 #13034953

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#10604614
unambiguous semidirect productD5⋊#1887

Splittings

FittingC2×C5×#127 ⋊ C4
SylowC5 ⋊ C2×#1887

Subgroups

subgroupG/H
centerC22#65779
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#127C4
socleC22×C5#386
prime radicalC2×D5×#127C2
cosocleC2×C4×D5C24
hypercenterC2×#127AGL(1,𝔽5)
hypocenterC5C2×#1887
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

2526 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 ofC2×#72221214, C2×AGL(1,𝔽5)×#453, #72221508, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#453, #72221508, #72221552, …
maximal quotient ofC2×#72221214, C2×#72213464, D3×#10604614, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105221);