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#347×C₁₅₁ #23751691

order	9664
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₅₁ · Schur multiplier (H₂) = C₁

Aliases

#347×C₁₅₁

Subgroups

	subgroup	G/H
center	C₄×C₁₅₁	C₄²
commutator	C₄	C₄²×C₁₅₁
Frattini, cosocle	C₂×C₈	C₂²×C₁₅₁
socle	C₂×C₁₅₁	#97
prime radical	C₂²×C₁₅₁	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₅₁ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3322 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34067142, #34067144, #347×D₁₅₁, …
maximal subgroup of	#1355×C₁₅₁, #1356×C₁₅₁, C₂×#347×C₁₅₁, …
maximal normal subgroup of	#1355×C₁₅₁, #1356×C₁₅₁, C₂×#347×C₁₅₁, …
maximal quotient of	#1313×C₁₅₁, #1375×C₁₅₁, C₂×#347×C₁₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9664, 28);