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#95×C₂₅₁ #22548571

order	8032
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₅₁ · Schur multiplier (H₂) = C₂³

Aliases

#95×C₂₅₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₅₁	C₂²
commutator	C₂	C₄²×C₂₅₁
Frattini, cosocle	C₂³	C₂²×C₂₅₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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	#30631420, #30631423, #95×D₂₅₁, …
maximal subgroup of	#327×C₂₅₁, #328×C₂₅₁, C₂×#95×C₂₅₁, …
maximal normal subgroup of	#327×C₂₅₁, #328×C₂₅₁, C₂×#95×C₂₅₁, …
maximal quotient of	#336×C₂₅₁, H(3,ℤ/4)×C₂₅₁, #338×C₂₅₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8032, 2);