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C₂²×C₁₆×C₁₆₃ #23781299

order	10432
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 124416
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₁₆×C₁₆₃
multiplicative	(ℤ/20872)ˣ, (ℤ/31308)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂³×C₁₆₃
socle, prime radical	C₂³×C₁₆₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10432 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35212613, #35212624, #35212628, …
maximal subgroup of	#1374×C₁₆₃, #1379×C₁₆₃, #1380×C₁₆₃, …
maximal normal subgroup of	#1374×C₁₆₃, #1379×C₁₆₃, #1380×C₁₆₃, …
maximal quotient of	C₂×C₄×C₁₆×C₁₆₃, C₂×C₂²⋊C₁₆×C₁₆₃, C₂×C₄⋊C₁₆×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 183);