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#347×C₁₃₁ #22552791

order	8384
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃₁ · Schur multiplier (H₂) = C₁

Aliases

#347×C₁₃₁

Subgroups

	subgroup	G/H
center	C₄×C₁₃₁	C₄²
commutator	C₄	C₄²×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₁
socle	C₂×C₁₃₁	#97
prime radical	C₂²×C₁₃₁	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₁ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2882 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30663993, #30663995, #347×D₁₃₁, …
maximal subgroup of	#1355×C₁₃₁, #1356×C₁₃₁, C₂×#347×C₁₃₁, …
maximal normal subgroup of	#1355×C₁₃₁, #1356×C₁₃₁, C₂×#347×C₁₃₁, …
maximal quotient of	#1313×C₁₃₁, #1375×C₁₃₁, C₂×#347×C₁₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 28);