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C₂×C₄×C₁₃×C₈₁ #72187294

order	8424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₁₃×C₈₁
multiplicative	(ℤ/8639)ˣ, (ℤ/12879)ˣ, (ℤ/17278)ˣ, (ℤ/25758)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₇	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₂×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₁₃×C₈₁, C₄²×C₁₃×C₈₁, C₂²×C₄×C₁₃×C₈₁, …
maximal normal subgroup of	C₂×C₈×C₁₃×C₈₁, C₄²×C₁₃×C₈₁, C₂²×C₄×C₁₃×C₈₁, …
maximal quotient of	C₂×C₈×C₁₃×C₈₁, C₄²×C₁₃×C₈₁, C₂²×C₄×C₁₃×C₈₁, …
automorphism group of	C₅₃×C₁₆₃, C₂×C₅₃×C₂₄₃
outer automorphism group of	C₅₃×C₁₆₃, C₂×C₅₃×C₂₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.