Finite Group Databasebeta

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D5×#60399 #72253554

order2560
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productD5×#60399

Splittings

FittingC5×#60399 ⋊ C2
SylowC5 ⋊ C2×#60399

Subgroups

subgroupG/H
centerC2C22×D5×#120
commutator, cosocleC23×C5C26
FrattiniC23C25×D5
FittingC5×#60399C2
socleC2×C5C23×#120
hypercenter#60399D5
hypocenterC5C2×#60399
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22×D4 ◁ #60399

46784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#6499874, AGL(1,𝔽5)×#60399, #72269870
maximal normal subgroup ofD5×#6499874, AGL(1,𝔽5)×#60399, #72269870

GAP

Past the SmallGroups library coverage — no SmallGroups id.