Finite Group Databasebeta

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C5×#10595100 #72230422

order2880
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#10595100

Splittings

FittingC2×C32×C5×D4 ⋊ C22
HallC32×C5 ⋊ C2×AGL(1,ℤ/8)
SylowC32 ⋊ C2×C5×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C5C2×#3811
commutator, cosocleC32×C4C24×C5
FrattiniC4C22×C5×D32
FittingC2×C32×C5×D4C22
socleC2×C32×C5C22×D4
hypercenterC2×C5×D4D32
hypocenterC32C2×C5×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×D4

1428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×#10595100
maximal normal subgroup ofD5×#10595100

GAP

Past the SmallGroups library coverage — no SmallGroups id.