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#330×C₁₃₁ #22552774

order	8384
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₁ · Schur multiplier (H₂) = C₁

Aliases

#330×C₁₃₁

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2489 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#330×D₁₃₁, #30664548, #30664554, …
maximal subgroup of	C₂×#330×C₁₃₁, #1524×C₁₃₁, #1526×C₁₃₁, …
maximal normal subgroup of	C₂×#330×C₁₃₁, #1524×C₁₃₁, #1526×C₁₃₁, …
maximal quotient of	#1271×C₁₃₁, #1295×C₁₃₁, C₂×#330×C₁₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8384, 11);