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#504×C₁₃₁ #22552948

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₁ · Schur multiplier (H₂) = C₂²

Aliases

#504×C₁₃₁

Subgroups

	subgroup	G/H
center	C₁₆×C₁₃₁	C₂²
commutator	C₂	C₂²×C₈×C₁₃₁
Frattini, cosocle	C₈	C₂³×C₁₃₁
socle	C₂×C₁₃₁	C₂²×C₈
prime radical	#41×C₁₃₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₃₁ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5240 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30664103, #30667796, #30667801, …
maximal subgroup of	#1401×C₁₃₁, #2170×C₁₃₁, #2171×C₁₃₁, …
maximal normal subgroup of	#1401×C₁₃₁, #2170×C₁₃₁, #2171×C₁₃₁, …
maximal quotient of	#2108×C₁₃₁, #2113×C₁₃₁, #2151×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 185);