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#14416802

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

Aliases

No aliases for this group.

Splittings

FittingC3×C5×D8 ⋊ C2×C4
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ #79865
SylowC3 ⋊ AGL(1,𝔽5)×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#911C2
cosocleC3×C4×D5C24
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ D8

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Polycyclic presentation:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), #72230460, #72259698
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8)
maximal quotient of#72230460, #72259698

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142500);