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#14425448

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

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×AGL(1,ℤ/8) ⋊ C2
HallC3×C5 ⋊ #3021
SylowC5 ⋊ #83957
SylowC3 ⋊ #10615688

Subgroups

subgroupG/H
centerC2C2×#91826
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC2×C3×C5C2×#120
hypercenterC2×AGL(1,ℤ/8)D15
hypocenterC3×C5#3021
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^7,3,5|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^2,i^c=i^4

Conjugacy classes & character table

183 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 151146);