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C2×AGL(1,𝔽5)×2−1+4 #13046017

order1280
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×AGL(1,𝔽5)×2−1+4
unambiguous semidirect productD5⋊(C4×2−1+4)

Splittings

FittingC2×C5×2−1+4 ⋊ C4
SylowC5 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC22C24×AGL(1,𝔽5)
commutatorC2×C5C25×C4
FrattiniC2C25×AGL(1,𝔽5)
FittingC2×C5×2−1+4C4
socleC22×C5C24×C4
prime radicalC2×D5×2−1+4C2
cosocleC2×D5C26
hypercenterC2×2−1+4AGL(1,𝔽5)
hypocenterC5C2×C4×2−1+4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116285);