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#95×C₁₆₃ #19104591

order	5216
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₆₃ · Schur multiplier (H₂) = C₂³

Aliases

#95×C₁₆₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₆₃	C₂²
commutator	C₂	C₄²×C₁₆₃
Frattini, cosocle	C₂³	C₂²×C₁₆₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₆₃ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3260 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#327×C₁₆₃, #328×C₁₆₃, C₂×#95×C₁₆₃, …
maximal normal subgroup of	#327×C₁₆₃, #328×C₁₆₃, C₂×#95×C₁₆₃, …
maximal quotient of	#336×C₁₆₃, H(3,ℤ/4)×C₁₆₃, #338×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5216, 2);