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C2×C3×D8×AGL(1,𝔽5) #14415994

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×D8×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C3×C4×D8)

Splittings

FittingC2×C3×C5×D8 ⋊ C4
HallC3×C5 ⋊ C2×C4×D8
SylowC5 ⋊ C2×C3×C4×D8

Subgroups

subgroupG/H
centerC22×C3D4×AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC2×C3×C5×D8C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D5×D8C2
cosocleC4×D5C24×C3
hypercenterC2×C3×D8AGL(1,𝔽5)
hypocenterC5C2×C3×C4×D8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D8

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×AGL(1,𝔽5)×AGL(1,𝔽7), C2×C3×AGL(1,𝔽5)×AGL(1,ℤ/8), C2×D3×D8×AGL(1,𝔽5)
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(1,ℤ/8), C2×D3×D8×AGL(1,𝔽5)
maximal quotient ofD8×AGL(1,𝔽5)×AGL(1,𝔽7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141692);