Finite Group Databasebeta

← Prev (#26040732) Next (#26040734) →

#322×C₁₈₁ #26040733

order	11584
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₈₁ · Schur multiplier (H₂) = C₄

Aliases

#322×C₁₈₁

Subgroups

	subgroup	G/H
center	C₄²×C₁₈₁	C₂²
commutator	C₂	C₄×C₈×C₁₈₁
Frattini, cosocle	C₄²	C₂²×C₁₈₁
socle, prime radical	C₂²×C₁₈₁	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₈₁ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7240 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37531642, #37531698, #322×D₁₈₁, …
maximal subgroup of	#1313×C₁₈₁, #1336×C₁₈₁, C₂×#322×C₁₈₁, …
maximal normal subgroup of	#1313×C₁₈₁, #1336×C₁₈₁, C₂×#322×C₁₈₁, …
maximal quotient of	#1273×C₁₈₁, #1312×C₁₈₁, #1313×C₁₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 3);