Finite Group Databasebeta

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#441×C₁₆₃ #23781238

order	10432
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₆₃ · Schur multiplier (H₂) = C₂²

Aliases

#441×C₁₆₃

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₆₃	C₂×D₄
commutator	C₄	C₂²×C₄×C₁₆₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₆₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₆₃ ◁ C₄²×C₁₆₃ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3586 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35216425, #441×D₁₆₃, #35223335, …
maximal subgroup of	#2180×C₁₆₃, C₂×#441×C₁₆₃, #2943×C₁₆₃, …
maximal normal subgroup of	#2180×C₁₆₃, C₂×#441×C₁₆₃, #2943×C₁₆₃, …
maximal quotient of	#1579×C₁₆₃, #1587×C₁₆₃, #1593×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 122);