Finite Group Databasebeta

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D5×#63926 #72230409

order2880
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productD5×#63926

Splittings

FittingC32×C5×D4 ⋊ C23
HallC32×C5 ⋊ C22×D8
SylowC32 ⋊ C2×D5×D8
SylowC5 ⋊ C2×#63926

Subgroups

subgroupG/H
centerC2D5×#3811
commutator, cosocleC32×C4×C5C24
FrattiniC4C2×D32×D5
FittingC32×C5×D4C23
socleC2×C32×C5C22×D4
hypercenterD4D32×D5
hypocenterC32×C5C22×D8
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ D4

1588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#63926, D5×#10595100, #72230444
maximal normal subgroup ofAGL(1,𝔽5)×#63926, D5×#10595100, #72230444

GAP

Past the SmallGroups library coverage — no SmallGroups id.