Finite Group Databasebeta

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C2×AGL(1,𝔽5)×#576 #72253192

order2560
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×AGL(1,𝔽5)×#576

Splittings

FittingC2×C5×#576 ⋊ C4
SylowC5 ⋊ C2×C4×#576

Subgroups

subgroupG/H
centerC22C22×D4×AGL(1,𝔽5)
commutatorC4×C5C25×C4
FrattiniC4C25×AGL(1,𝔽5)
FittingC2×C5×#576C4
socleC22×C5C22×C4×D4
prime radicalC2×D5×#576C2
cosocleC4×D5C26
hypercenterC2×#576AGL(1,𝔽5)
hypocenterC5C2×C4×#576
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

21824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.