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D5×#6474 #72218012

order2240
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD5×#6474

Splittings

FittingC5×C7×D8 ⋊ C22
HallC5×C7 ⋊ C2×AGL(1,ℤ/8)
SylowC7 ⋊ D5×AGL(1,ℤ/8)
SylowC5 ⋊ C2×#6474

Subgroups

subgroupG/H
centerC2D4×D5×D7
commutator, cosocleC4×C5×C7C24
FrattiniC4C22×D5×D7
FittingC5×C7×D8C22
socleC2×C5×C7C22×D4
hypercenterD8D5×D7
hypocenterC5×C7C2×AGL(1,ℤ/8)
LCSG ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2 ◁ C4 ◁ D8

596 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#6474⋊C3, D5×D7×AGL(1,ℤ/8), AGL(1,𝔽5)×#6474, …
maximal normal subgroup ofD5×#6474⋊C3, D5×D7×AGL(1,ℤ/8), AGL(1,𝔽5)×#6474, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.