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D7×AGL(1,𝔽5)×AGL(1,𝔽9) #72217487

order20160
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productD7×AGL(1,𝔽5)×AGL(1,𝔽9)

Splittings

Fitting, socle, derived, HallC32×C5×C7 ⋊ C2×C4×C8
HallC32×C7 ⋊ C2×C8×AGL(1,𝔽5)
HallC32×C5 ⋊ C4×C8×D7
HallC5×C7 ⋊ C2×C4×AGL(1,𝔽9)
SylowC32 ⋊ C8×D7×AGL(1,𝔽5)
SylowC7 ⋊ C2×AGL(1,𝔽5)×AGL(1,𝔽9)
SylowC5 ⋊ C4×D7×AGL(1,𝔽9)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C7C2×C4×C8
prime radicalD5×D7×C3⋊D3C2×C4
cosocleC7×D5×#157C23
LCSG ▷ C32×C5×C7
UCSC1

756 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,𝔽7)×AGL(1,𝔽9)
maximal normal subgroup ofAGL(1,𝔽5)×AGL(1,𝔽7)×AGL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.