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C2×C5×#5199 #14429373

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#5199

Splittings

FittingC2×C3×C5×AGL(1,ℤ/8) ⋊ C2
HallC3×C5 ⋊ C2×#472
SylowC3 ⋊ C2×C5×#472

Subgroups

subgroupG/H
centerC22×C5#939
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5#121
hypercenterC2×C5×AGL(1,ℤ/8)D3
hypocenterC3C2×C5×#472
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×AGL(1,ℤ/8)

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 155071);