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#338×C₁₅₁ #23751682

order	9664
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₅₁ · Schur multiplier (H₂) = C₂²

Aliases

#338×C₁₅₁

Subgroups

	subgroup	G/H
center	C₄×C₁₅₁	C₄²
commutator	C₄	C₄²×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂²×C₁₅₁
socle	C₂×C₁₅₁	#95
prime radical	C₂³×C₁₅₁	Q₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₅₁ ◁ G

86 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	#34067100, #34067103, #338×D₁₅₁, …
maximal subgroup of	#1341×C₁₅₁, #1342×C₁₅₁, C₂×#338×C₁₅₁, …
maximal normal subgroup of	#1341×C₁₅₁, #1342×C₁₅₁, C₂×#338×C₁₅₁, …
maximal quotient of	#1275×C₁₅₁, #1291×C₁₅₁, #1292×C₁₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9664, 19);