Finite Group Databasebeta

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C4×D7×GO+(4,𝔽2) #72217884

order4032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×D7×GO+(4,𝔽2)

Splittings

FittingC32×C4×C7 ⋊ C2×D4
HallC32×C7 ⋊ C2×C4×D4
SylowC32 ⋊ C4×D4×D7
SylowC7 ⋊ C2×C4×GO+(4,𝔽2)

Subgroups

subgroupG/H
center, hypercenterC4D7×GO+(4,𝔽2)
commutatorC7×C3⋊D3C23×C4
FrattiniC2C2×D7×GO+(4,𝔽2)
FittingC32×C4×C7C2×D4
socleC2×C32×C7C22×D4
prime radicalC2×D7×GO+(4,𝔽2)C2
cosocleC2×C7×C3⋊D3C24
hypocenterC32×C7C2×C4×D4
LCSG ▷ C7×C3⋊D3 ▷ C32×C7
UCSC1 ◁ C4

1324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×AGL(1,𝔽7)×GO+(4,𝔽2)
maximal normal subgroup ofC4×AGL(1,𝔽7)×GO+(4,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.