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C2×#10604492 #13034886

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#10604492
unambiguous semidirect productD5⋊#1875

Splittings

FittingC2×C5×#121 ⋊ C4
SylowC5 ⋊ C2×#1875

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#121C4
socleC23×C5C2×C22⋊C4
prime radicalC2×D5×#121C2
cosocleC2×C4×D5C24
hypercenterC2×#121AGL(1,𝔽5)
hypocenterC5C2×#1875
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

2310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1105154);