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#568×C₁₃₁ #22553012

order	8384
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

#568×C₁₃₁

Subgroups

	subgroup	G/H
center	C₄×C₁₃₁	C₂⁴
commutator	C₂	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₄	C₂⁴×C₁₃₁
socle	C₂×C₁₃₁	C₂³×C₄
prime radical	C₂×#41×C₁₃₁	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₁ ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4454 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30666181, #30666201, #30666247, …
maximal subgroup of	#1858×C₁₃₁, #1861×C₁₃₁, #1868×C₁₃₁, …
maximal normal subgroup of	#1858×C₁₃₁, #1861×C₁₃₁, #1868×C₁₃₁, …
maximal quotient of	#2873×C₁₃₁, #2875×C₁₃₁, #2879×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 249);