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C₂×AGL(1,ℤ/32) #72216318

order	1024
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×AGL(1,ℤ/32)

Subgroups

	subgroup	G/H
center, socle	C₂²	#12067
commutator	C₁₆	C₂³×C₈
Frattini, cosocle	#346	C₂⁴
prime radical	C₂×#2263	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#1313 ◁ G
LECS	G ▷ #346 ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

649 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

94 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72216335, D₃×AGL(1,ℤ/32), C₄×AGL(1,ℤ/32), …
maximal normal subgroup of	#72216335, C₄×AGL(1,ℤ/32), C₂²×AGL(1,ℤ/32), …
maximal quotient of	D₃×AGL(1,ℤ/32), C₄×AGL(1,ℤ/32), C₂²×AGL(1,ℤ/32), …
automorphism group of	#1425, #2262, C₃×D₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.