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C4×D7×AGL(1,ℤ/8) #14217852

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×D7×AGL(1,ℤ/8)

Splittings

FittingC4×C7×AGL(1,ℤ/8) ⋊ C2
SylowC7 ⋊ C2×C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC4×C7×AGL(1,ℤ/8)C2
socleC22×C7C23×D4
prime radicalC2×D7×AGL(1,ℤ/8)C2
cosocleC2×C4×C7C25
hypercenterC4×AGL(1,ℤ/8)D7
hypocenterC7C2×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

3242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×AGL(1,𝔽5)×AGL(1,ℤ/8), C4×AGL(1,ℤ/8)×AGL(1,𝔽7)
maximal normal subgroup ofC4×AGL(1,ℤ/8)×AGL(1,𝔽7)
maximal quotient ofD7×AGL(1,𝔽5)×AGL(1,ℤ/8)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1033624);