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#347×C₁₀₁ #20264656

order	6464
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₁ · Schur multiplier (H₂) = C₁

Aliases

#347×C₁₀₁

Subgroups

	subgroup	G/H
center	C₄×C₁₀₁	C₄²
commutator	C₄	C₄²×C₁₀₁
Frattini, cosocle	C₂×C₈	C₂²×C₁₀₁
socle	C₂×C₁₀₁	#97
prime radical	C₂²×C₁₀₁	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₁ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2222 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#1355, C₁₀₁×#1356, C₂×#347×C₁₀₁, …
maximal normal subgroup of	C₁₀₁×#1355, C₁₀₁×#1356, C₂×#347×C₁₀₁, …
maximal quotient of	C₁₀₁×#1313, C₁₀₁×#1375, C₂×#347×C₁₀₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6464, 28);