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C₂×C₂²⋊C₈×C₁₃₁ #22552850

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₁ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₂²⋊C₈×C₁₃₁

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃₁	C₂²
commutator	C₂	C₂²×C₈×C₁₃₁
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₁
socle	C₂³×C₁₃₁	C₂×C₄
prime radical	C₂⁴×C₁₃₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

202 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	#30663803, #30663807, #30663808, …
maximal subgroup of	#1280×C₁₃₁, #1282×C₁₃₁, #1289×C₁₃₁, …
maximal normal subgroup of	#1280×C₁₃₁, #1282×C₁₃₁, #1289×C₁₃₁, …
maximal quotient of	C₂×#323×C₁₃₁, C₂×#324×C₁₃₁, #1458×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 87);