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#376×C₁₃₁ #22552820

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₃₁ · Schur multiplier (H₂) = C₂×C₄²

Aliases

#376×C₁₃₁

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂²
commutator	C₂	C₂×C₄²×C₁₃₁
Frattini, cosocle	C₂³	C₂³×C₁₃₁
socle, prime radical	C₂³×C₁₃₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

178 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	#30663790, #30663854, #30664445, …
maximal subgroup of	#1274×C₁₃₁, #1300×C₁₃₁, #1500×C₁₃₁, …
maximal normal subgroup of	#1274×C₁₃₁, #1300×C₁₃₁, #1500×C₁₃₁, …
maximal quotient of	C₄×#95×C₁₃₁, #1434×C₁₃₁, #1744×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 57);