Finite Group Databasebeta

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D5×#8534 #72243215

order2560
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productD5×#8534

Splittings

FittingC5×#8534 ⋊ C2
SylowC5 ⋊ C2×#8534

Subgroups

subgroupG/H
centerC22D5×#379
commutatorC24×C5C23×C4
FrattiniC25C23×D5
FittingC5×#8534C2
socleC22×C5C2×#379
prime radicalD5×#3484C2
cosocleC25×C5C24
hypercenter#8534D5
hypocenterC5C2×#8534
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C25 ◁ #8534

9744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72243234, AGL(1,𝔽5)×#8534, D5×#347042
maximal normal subgroup of#72243234, AGL(1,𝔽5)×#8534, D5×#347042

GAP

Past the SmallGroups library coverage — no SmallGroups id.