Finite Group Databasebeta

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D7×#65731 #72218544

order4480
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD7×#65731

Splittings

FittingC5×C7×D8 ⋊ C2×C4
HallC5×C7 ⋊ C2×#442
SylowC7 ⋊ C2×#65731
SylowC5 ⋊ D7×#442

Subgroups

subgroupG/H
centerC2D4×D7×AGL(1,𝔽5)
commutatorC4×C5×C7C23×C4
FrattiniC4C22×D7×AGL(1,𝔽5)
FittingC5×C7×D8C2×C4
socleC2×C5×C7C2×C4×D4
prime radicalD5×D7×D8C2
cosocleC4×C7×D5C24
hypercenterD8D7×AGL(1,𝔽5)
hypocenterC5×C7C2×#442
LCSG ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C4 ◁ D8

1216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#65731, D7×AGL(1,𝔽5)×AGL(1,ℤ/8)
maximal normal subgroup ofAGL(1,𝔽7)×#65731, D7×AGL(1,𝔽5)×AGL(1,ℤ/8)

GAP

Past the SmallGroups library coverage — no SmallGroups id.