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C3×C5×#949 #13087960

order1440
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC3×C5×#949

Splittings

FittingC32×C5×#41 ⋊ C2
HallC32×C5 ⋊ AGL(1,ℤ/8)
SylowC32 ⋊ C5×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C3×C5C2×#67
commutator, cosocleC3×C4C23×C3×C5
FrattiniC4C22×C3×C5×D3
FittingC32×C5×#41C2
socleC2×C32×C5C2×D4
hypercenterC3×C5×#41D3
hypocenterC3C3×C5×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C5 ◁ C2×C3×C4×C5 ◁ C3×C5×#41

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4277);