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C3×#10615688 #14425447

order1920
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC3×#10615688

Splittings

FittingC2×C3×C5×AGL(1,ℤ/8) ⋊ C2
HallC3×C5 ⋊ #3021
SylowC5 ⋊ C3×#3021

Subgroups

subgroupG/H
centerC2×C3C2×#4083
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC2×C3×C5C2×#120
hypercenterC2×C3×AGL(1,ℤ/8)D5
hypocenterC5C3×#3021
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

1472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 151145);