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D₄⋊C₈×C₁₆₃ #23781122

order	10432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₆₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₄⋊C₈×C₁₆₃
unambiguous semidirect product	D₄⋊(C₈×C₁₆₃)

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₆₃	D₄
commutator	C₄	C₂×C₈×C₁₆₃
Frattini, cosocle	C₄²	C₂²×C₁₆₃
socle	C₂²×C₁₆₃	C₂²⋊C₄
prime radical	C₂×D₄×C₁₆₃	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₆₃ ◁ C₄²×C₁₆₃ ◁ G

82 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	D₄⋊C₈×D₁₆₃, #35212915, #35212920, …
maximal subgroup of	C₂×D₄⋊C₈×C₁₆₃, #1476×C₁₆₃, #1477×C₁₆₃, …
maximal normal subgroup of	C₂×D₄⋊C₈×C₁₆₃, #1476×C₁₆₃, #1477×C₁₆₃, …
maximal quotient of	#1270×C₁₆₃, #1271×C₁₆₃, #1279×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 6);