Finite Group Databasebeta

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D5×#3151 #12968740

order1280
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productD5×#3151

Splittings

FittingC5×#3151 ⋊ C2
SylowC5 ⋊ C2×#3151

Subgroups

subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3151C2
socleC22×C5C23×D4
hypercenter#3151D5
hypocenterC5C2×#3151
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5⋊D5×#3151, AGL(1,𝔽5)×#3151, D5×#19745, …
maximal normal subgroup ofAGL(1,𝔽5)×#3151, D5×#19745, #72221440, …
maximal quotient ofC5⋊D5×#3151, D5×#19745, #72226589

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1039008);