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C₂×C₄×Q₈×C₁₃₁ #22552960

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₃₁

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂²
commutator	C₂	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²	C₂⁴×C₁₃₁
socle, prime radical	C₂³×C₁₃₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

298 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	#30664285, #30664305, C₂×Q₈⋊(C₁₃₁⋊C₈), …
maximal subgroup of	#1461×C₁₃₁, #1467×C₁₃₁, C₂×Q₈⋊C₈×C₁₃₁, …
maximal normal subgroup of	#1461×C₁₃₁, #1467×C₁₃₁, C₂×Q₈⋊C₈×C₁₃₁, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₃₁, C₄²×Q₈×C₁₃₁, C₂×#387×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 197);