Finite Group Databasebeta

← Prev (#22552781) Next (#22552783) →

#338×C₁₃₁ #22552782

order	8384
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃₁ · Schur multiplier (H₂) = C₂²

Aliases

#338×C₁₃₁

Subgroups

	subgroup	G/H
center	C₄×C₁₃₁	C₄²
commutator	C₄	C₄²×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂²×C₁₃₁
socle	C₂×C₁₃₁	#95
prime radical	C₂³×C₁₃₁	Q₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₁ ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2882 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30663951, #30663954, #338×D₁₃₁, …
maximal subgroup of	#1341×C₁₃₁, #1342×C₁₃₁, C₂×#338×C₁₃₁, …
maximal normal subgroup of	#1341×C₁₃₁, #1342×C₁₃₁, C₂×#338×C₁₃₁, …
maximal quotient of	#1275×C₁₃₁, #1291×C₁₃₁, #1292×C₁₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 19);