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D₄⋊C₈×C₁₃₁ #22552769

order	8384
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product	D₄⋊C₈×C₁₃₁
unambiguous semidirect product	D₄⋊(C₈×C₁₃₁)

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃₁	D₄
commutator	C₄	C₂×C₈×C₁₃₁
Frattini, cosocle	C₄²	C₂²×C₁₃₁
socle	C₂²×C₁₃₁	C₂²⋊C₄
prime radical	C₂×D₄×C₁₃₁	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₄²×C₁₃₁ ◁ G

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3668 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	D₄⋊C₈×D₁₃₁, #30664340, #30664345, …
maximal subgroup of	C₂×D₄⋊C₈×C₁₃₁, #1476×C₁₃₁, #1477×C₁₃₁, …
maximal normal subgroup of	C₂×D₄⋊C₈×C₁₃₁, #1476×C₁₃₁, #1477×C₁₃₁, …
maximal quotient of	#1270×C₁₃₁, #1271×C₁₃₁, #1279×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 6);