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C5×Dic3×AGL(1,ℤ/8) #14416661

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×Dic3×AGL(1,ℤ/8)

Splittings

HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC3 ⋊ C4×C5×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×AGL(1,ℤ/8)D3
hypocenterC3C4×C5×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×AGL(1,ℤ/8)

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142359);