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C₈×D₄×C₁₆₃ #23781231

order	10432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₆₃ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₄×C₁₆₃

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₆₃	C₂²
commutator	C₂	C₂²×C₈×C₁₆₃
Frattini, cosocle	C₂×C₄	C₂³×C₁₆₃
socle	C₂²×C₁₆₃	C₂²×C₄
prime radical	C₂×D₄×C₁₆₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₆₃ ◁ G

134 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	D₄⋊(C₁₆₃⋊C₁₆), C₈×#14579684, C₈×#14579687, …
maximal subgroup of	D₄⋊C₁₆×C₁₆₃, C₈×D₈×C₁₆₃, C₈×SD₁₆×C₁₆₃, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₆₃, C₈×D₈×C₁₆₃, C₈×SD₁₆×C₁₆₃, …
maximal quotient of	C₈×D₈×C₁₆₃, C₈×SD₁₆×C₁₆₃, C₈×Q₁₆×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 115);