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C₈×Q₈×C₁₆₃ #23781242

order	10432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₆₃ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₆₃

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₆₃	C₂²
commutator	C₂	C₂²×C₈×C₁₆₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₆₃
socle, prime radical	C₂²×C₁₆₃	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₆₃ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6520 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Q₈⋊(C₁₆₃⋊C₁₆), C₈×#14579686, C₈×#14579689, …
maximal subgroup of	Q₈⋊C₁₆×C₁₆₃, C₈×SD₁₆×C₁₆₃, C₈×Q₁₆×C₁₆₃, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₆₃, C₈×SD₁₆×C₁₆₃, C₈×Q₁₆×C₁₆₃, …
maximal quotient of	C₈×C₄⋊C₄×C₁₆₃, #1916×C₁₆₃, #1939×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 126);