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C3×AGL(1,𝔽5)×AGL(1,ℤ/8) #14416673

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×AGL(1,𝔽5)×AGL(1,ℤ/8)

Splittings

FittingC3×C5×AGL(1,ℤ/8) ⋊ C4
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ C3×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C3C2×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC3×C5×AGL(1,ℤ/8)C4
socleC2×C3×C5C2×C4×D4
prime radicalC3×D5×AGL(1,ℤ/8)C2
cosocleC4×D5C24×C3
hypercenterC3×AGL(1,ℤ/8)AGL(1,𝔽5)
hypocenterC5C3×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×AGL(1,ℤ/8)

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×AGL(1,ℤ/8), AGL(1,ℤ/8)×ΓL(1,𝔽8)⋊AGL(1,𝔽5), AGL(1,𝔽5)×#6474⋊C3, …
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(1,ℤ/8), C3×AGL(1,𝔽5)×#453, D3×AGL(1,𝔽5)×AGL(1,ℤ/8), …
maximal quotient ofAGL(1,𝔽5)×ΓL(1,𝔽8)×AGL(1,ℤ/8), AGL(1,ℤ/8)×ΓL(1,𝔽8)⋊AGL(1,𝔽5), AGL(1,𝔽5)×#6474⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142371);