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AΣL(1,𝔽₁₆)×C₁₅₁ #23751695

order	9664
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₅₁ · Schur multiplier (H₂) = C₂²

Aliases

AΣL(1,𝔽₁₆)×C₁₅₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₅₁	#99
commutator	C₂³	C₂×C₄×C₁₅₁
Frattini, cosocle	C₂×D₄	C₂²×C₁₅₁
prime radical	#120×C₁₅₁	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₁ ◁ C₂²×C₁₅₁ ◁ C₂×D₄×C₁₅₁ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1963 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	AΣL(1,𝔽₁₆)×D₁₅₁, #34070748, #34070753, …
maximal subgroup of	C₂×AΣL(1,𝔽₁₆)×C₁₅₁, #2120×C₁₅₁, #2121×C₁₅₁, …
maximal normal subgroup of	C₂×AΣL(1,𝔽₁₆)×C₁₅₁, #2120×C₁₅₁, #2121×C₁₅₁, …
maximal quotient of	#1316×C₁₅₁, #1326×C₁₅₁, #1343×C₁₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9664, 32);