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C₂²⋊C₁₆×C₁₅₁ #23751692

order	9664
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₅₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₁₆×C₁₅₁
unambiguous semidirect product	C₂²⋊(C₁₆×C₁₅₁)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₅₁	C₂²
commutator	C₂	C₂×C₁₆×C₁₅₁
Frattini, cosocle	C₂×C₈	C₂²×C₁₅₁
socle	C₂²×C₁₅₁	C₂×C₈
prime radical	C₂³×C₁₅₁	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₅₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6040 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34067033, #34067035, #34067049, …
maximal subgroup of	#1314×C₁₅₁, #1315×C₁₅₁, #1322×C₁₅₁, …
maximal normal subgroup of	#1314×C₁₅₁, #1315×C₁₅₁, #1322×C₁₅₁, …
maximal quotient of	#1314×C₁₅₁, #1322×C₁₅₁, D₄⋊C₁₆×C₁₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9664, 29);