Finite Group Databasebeta

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D7×#65727 #72218569

order4480
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD7×#65727

Splittings

FittingC5×C7×M16 ⋊ C2×C4
HallC5×C7 ⋊ C2×#428
SylowC7 ⋊ C2×#65727
SylowC5 ⋊ D7×#428

Subgroups

subgroupG/H
centerC2C2×D7×C4⋊AGL(1,𝔽5)
commutatorC4×C5×C7C23×C4
FrattiniC4C22×D7×AGL(1,𝔽5)
FittingC5×C7×M16C2×C4
socleC2×C5×C7C22×C4⋊C4
prime radicalC22×D5×D7D4
cosocleC4×C7×D5C24
hypercenterM16D7×AGL(1,𝔽5)
hypocenterC5×C7C2×#428
LCSG ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

1072 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#65727, D7×AGL(1,𝔽5)×AGL(1,ℤ/8)
maximal normal subgroup ofAGL(1,𝔽7)×#65727, D7×AGL(1,𝔽5)×AGL(1,ℤ/8)

GAP

Past the SmallGroups library coverage — no SmallGroups id.