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C₈×Q₈×C₁₃₁ #22552889

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₁ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₃₁

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃₁	C₂²
commutator	C₂	C₂²×C₈×C₁₃₁
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₁
socle, prime radical	C₂²×C₁₃₁	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₁ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5240 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Q₈⋊(C₁₃₁⋊C₁₆), C₈×#14523500, C₈×#14523503, …
maximal subgroup of	Q₈⋊C₁₆×C₁₃₁, C₈×SD₁₆×C₁₃₁, C₈×Q₁₆×C₁₃₁, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₃₁, C₈×SD₁₆×C₁₃₁, C₈×Q₁₆×C₁₃₁, …
maximal quotient of	C₈×C₄⋊C₄×C₁₃₁, #1916×C₁₃₁, #1939×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 126);