Finite Group Databasebeta

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C₂×C₂₀₄₈ #72183622

order	4096
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4096
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₂₀₄₈
multiplicative	(ℤ/8192)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₀₂₄	C₂²
socle, prime radical	C₂²	C₁₀₂₄
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₁₀₂₄ ▷ C₅₁₂ ▷ C₂₅₆ ▷ C₁₂₈ ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

35 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄₀₉₆, C₄×C₂₀₄₈, C₂²×C₂₀₄₈, …
maximal normal subgroup of	C₂×C₄₀₉₆, C₄×C₂₀₄₈, C₂²×C₂₀₄₈, …
maximal quotient of	C₂×C₄₀₉₆, C₄×C₂₀₄₈, C₂²×C₂₀₄₈, …
automorphism group of	C₈₁₉₂
outer automorphism group of	C₈₁₉₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.