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C₂×C₈₁₉₂ #72194294

order	16384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₈₁₉₂
multiplicative	(ℤ/32768)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄₀₉₆	C₂²
socle, prime radical	C₂²	C₄₀₉₆
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₄₀₉₆ ▷ C₂₀₄₈ ▷ C₁₀₂₄ ▷ C₅₁₂ ▷ C₂₅₆ ▷ C₁₂₈ ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

41 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₆₃₈₄, C₄×C₈₁₉₂, C₂²×C₈₁₉₂, …
maximal normal subgroup of	C₂×C₁₆₃₈₄, C₄×C₈₁₉₂, C₂²×C₈₁₉₂, …
maximal quotient of	C₂×C₁₆₃₈₄, C₄×C₈₁₉₂, C₂²×C₈₁₉₂, …
automorphism group of	C₃₂₇₆₈
outer automorphism group of	C₃₂₇₆₈

GAP

Past the SmallGroups library coverage — no SmallGroups id.