Finite Group Databasebeta

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C₂×C₅₁₂ #72181925

order	1024
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1024
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₅₁₂
multiplicative	(ℤ/2048)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅₆	C₂²
socle, prime radical	C₂²	C₂₅₆
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂₅₆ ▷ C₁₂₈ ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

29 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₂₄, C₄×C₅₁₂, C₂²×C₅₁₂, …
maximal normal subgroup of	C₂×C₁₀₂₄, C₄×C₅₁₂, C₂²×C₅₁₂, …
maximal quotient of	C₂×C₁₀₂₄, C₄×C₅₁₂, C₂²×C₅₁₂, …
automorphism group of	C₂₀₄₈
outer automorphism group of	C₂₀₄₈

GAP

Past the SmallGroups library coverage — no SmallGroups id.