Finite Group Databasebeta

← Prev (#72186753) Next (#72186755) →

C₂²×C₃×C₄×C₁₆₃ #72186754

order	7824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 62208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₃×C₄×C₁₆₃
multiplicative	(ℤ/13713)ˣ, (ℤ/18284)ˣ, (ℤ/23508)ˣ, (ℤ/27426)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃×C₁₆₃
socle, prime radical	C₂³×C₃×C₁₆₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄²×C₁₆₃, C₂²×C₃×C₈×C₁₆₃, C₂³×C₃×C₄×C₁₆₃, …
maximal normal subgroup of	C₂×C₃×C₄²×C₁₆₃, C₂²×C₃×C₈×C₁₆₃, C₂³×C₃×C₄×C₁₆₃, …
maximal quotient of	C₂×C₃×C₄²×C₁₆₃, C₂²×C₃×C₈×C₁₆₃, C₂³×C₃×C₄×C₁₆₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.