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#446×C₁₆₃ #23781243

order	10432
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₆₃ · Schur multiplier (H₂) = C₂

Aliases

#446×C₁₆₃

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₆₃	C₂³
commutator	C₂²	C₂²×C₄×C₁₆₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₆₃
socle, prime radical	C₂²×C₁₆₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₆₃ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4564 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35212518, #35213370, #35213384, …
maximal subgroup of	#1338×C₁₆₃, #1582×C₁₆₃, #1584×C₁₆₃, …
maximal normal subgroup of	#1338×C₁₆₃, #1582×C₁₆₃, #1584×C₁₆₃, …
maximal quotient of	#1770×C₁₆₃, #1771×C₁₆₃, #1916×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 127);