Finite Group Databasebeta

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#504×C₁₆₃ #23781301

order	10432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₆₃ · Schur multiplier (H₂) = C₂²

Aliases

#504×C₁₆₃

Subgroups

	subgroup	G/H
center	C₁₆×C₁₆₃	C₂²
commutator	C₂	C₂²×C₈×C₁₆₃
Frattini, cosocle	C₈	C₂³×C₁₆₃
socle	C₂×C₁₆₃	C₂²×C₈
prime radical	#41×C₁₆₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₆₃ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6520 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35212678, #35216371, #35216376, …
maximal subgroup of	#1401×C₁₆₃, #2170×C₁₆₃, #2171×C₁₆₃, …
maximal normal subgroup of	#1401×C₁₆₃, #2170×C₁₆₃, #2171×C₁₆₃, …
maximal quotient of	#2108×C₁₆₃, #2113×C₁₆₃, #2151×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 185);