Finite Group Databasebeta

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D7×#4130 #72218426

order2240
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD7×#4130

Splittings

FittingC2×C4×C5×C7 ⋊ C2×C4
HallC5×C7 ⋊ C2×#117
SylowC7 ⋊ C2×#4130
SylowC5 ⋊ D7×#117

Subgroups

subgroupG/H
centerC4C2×D7×AGL(1,𝔽5)
commutator, socleC2×C5×C7C23×C4
FrattiniC2C22×D7×AGL(1,𝔽5)
FittingC2×C4×C5×C7C2×C4
prime radicalC22×D5×D7C22
cosocleC2×C7×D5C24
hypercenterC2×C4D7×AGL(1,𝔽5)
hypocenterC5×C7C2×#117
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C4 ◁ C2×C4

660 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#4130, D7×#65727, D7×#65767, …
maximal normal subgroup ofAGL(1,𝔽7)×#4130, D7×#65727, D7×#65767, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.