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C22×AGL(1,ℤ/32) #72223722

order2048
nilpotency class5
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×AGL(1,ℤ/32)

Subgroups

subgroupG/H
center, socleC23#12067
commutatorC16C24×C8
Frattini, cosocle#346C25
prime radicalC22×#2263C4
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×C8 ◁ C22×#1313 ◁ G
LECSG ▷ #346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

3960 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofA4×AGL(1,ℤ/32), S4×AGL(1,ℤ/32)
maximal subgroup ofC2×C4×AGL(1,ℤ/32), C2×D3×AGL(1,ℤ/32), C2×#72225052, …
maximal normal subgroup ofC2×C4×AGL(1,ℤ/32), C2×#72225052, C23×AGL(1,ℤ/32), …
maximal quotient ofC2×C4×AGL(1,ℤ/32), C2×D3×AGL(1,ℤ/32), C2×#72225052, …
automorphism group of#13655

GAP

Past the SmallGroups library coverage — no SmallGroups id.