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C₂²×C₂²⋊C₄×C₁₃₁ #22552956

order	8384
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₁ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂²×C₂²⋊C₄×C₁₃₁

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₃₁	C₂²
commutator	C₂	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²	C₂⁴×C₁₃₁
prime radical	C₂⁵×C₁₃₁	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₁ ◁ G

674 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	#30664183, #30664198, #30664200, …
maximal subgroup of	C₂²⋊#95×C₁₃₁, #1437×C₁₃₁, #1438×C₁₃₁, …
maximal normal subgroup of	C₂²⋊#95×C₁₃₁, #1437×C₁₃₁, #1438×C₁₃₁, …
maximal quotient of	C₂²×#95×C₁₃₁, C₂×C₄×C₂²⋊C₄×C₁₃₁, C₂×#379×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 193);