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AGL(1,𝔽5)×#908 #14416809

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

Aliases

direct productAGL(1,𝔽5)×#908

Splittings

FittingC3×C5×M16 ⋊ C2×C4
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ C4×#908
SylowC3 ⋊ AGL(1,𝔽5)×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2C2×AGL(1,𝔽5)×D12
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×M16C2×C4
socleC2×C3×C5C2×C4×D4
prime radicalD5×#908C2
cosocleC3×C4×D5C24
hypercenterM16D3×AGL(1,𝔽5)
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), AGL(1,𝔽5)×#4822, AGL(1,𝔽5)×#63825, …
maximal normal subgroup ofD3×AGL(1,𝔽5)×AGL(1,ℤ/8), AGL(1,𝔽5)×#4822, AGL(1,𝔽5)×#4747
maximal quotient ofAGL(1,𝔽5)×#63825, #72230948

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142507);