Finite Group Databasebeta

← Prev (#72187473) Next (#72187475) →

C₂×C₄×C₁₃×C₈₃ #72187474

order	8632
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7872
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₁₃×C₈₃
multiplicative	(ℤ/8851)ˣ, (ℤ/17702)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₁₃×C₈₃
socle, prime radical	C₂²×C₁₃×C₈₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8632 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₁₃×C₈₃, C₄²×C₁₃×C₈₃, C₂²×C₄×C₁₃×C₈₃, …
maximal normal subgroup of	C₂×C₈×C₁₃×C₈₃, C₄²×C₁₃×C₈₃, C₂²×C₄×C₁₃×C₈₃, …
maximal quotient of	C₂×C₈×C₁₃×C₈₃, C₄²×C₁₃×C₈₃, C₂²×C₄×C₁₃×C₈₃, …
automorphism group of	C₅₃×C₁₆₇
outer automorphism group of	C₅₃×C₁₆₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.