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AGL(1,ℤ/8)×AGL(2,𝔽3) #72220248

order13824
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/8)×AGL(2,𝔽3)

Splittings

FittingC32×AGL(1,ℤ/8) ⋊ GL(2,𝔽3)

Subgroups

subgroupG/H
centerC2C2×D4×AGL(2,𝔽3)
commutator, cosocleC4×PSU(3,𝔽2)⋊C3C24
FrattiniC4C23×AGL(2,𝔽3)
FittingC32×AGL(1,ℤ/8)GL(2,𝔽3)
socleC2×C32C2×D4×GL(2,𝔽3)
hypercenterAGL(1,ℤ/8)AGL(2,𝔽3)
hypocenterPSU(3,𝔽2)⋊C3C2×AGL(1,ℤ/8)
LCSG ▷ C4×PSU(3,𝔽2)⋊C3 ▷ C2×PSU(3,𝔽2)⋊C3 ▷ PSU(3,𝔽2)⋊C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

7630 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

automorphism group of#3745, #3746
holomorph ofC32×C8

GAP

Past the SmallGroups library coverage — no SmallGroups id.