Finite Group Databasebeta

← Prev (#22548592) Next (#22548594) →

#117×C₂₅₁ #22548593

order	8032
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₅₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₂₅₁

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₅₁	C₂²
commutator	C₂	C₂²×C₄×C₂₅₁
Frattini, cosocle	C₂²	C₂³×C₂₅₁
socle	C₂²×C₂₅₁	C₂³
prime radical	C₂³×C₂₅₁	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₅₁ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5020 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30631443, #30631446, #30631457, …
maximal subgroup of	H(3,ℤ/4)×C₂₅₁, #339×C₂₅₁, #344×C₂₅₁, …
maximal normal subgroup of	H(3,ℤ/4)×C₂₅₁, #339×C₂₅₁, #344×C₂₅₁, …
maximal quotient of	#376×C₂₅₁, C₄×C₂²⋊C₄×C₂₅₁, C₄×C₄⋊C₄×C₂₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8032, 24);