Finite Group Databasebeta

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C₂×#483590 #72223586

order	1024
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

Subgroups

	subgroup	G/H
center	C₂²×C₄	#442
commutator	C₈	C₂⁴×C₈
Frattini, cosocle	C₄×C₈	C₂⁵
socle	C₂³	C₂×#442
prime radical	C₂²×#509	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#322 ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

3237 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₈×AGL(1,ℤ/16), C₂×#72216441, C₂×#72216771, …
maximal normal subgroup of	C₂×C₈×AGL(1,ℤ/16), C₂×#72216441, C₂×#72216771, …
maximal quotient of	C₂×C₄×#12067, C₂×#72225051, #72286009, …
automorphism group of	#7387

GAP

Past the SmallGroups library coverage — no SmallGroups id.