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#131×C₂₆₃ #22554362

order	8416
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₆₃ · Schur multiplier (H₂) = C₂²

Aliases

#131×C₂₆₃

Subgroups

	subgroup	G/H
center	C₈×C₂₆₃	C₂²
commutator	C₂	C₂²×C₄×C₂₆₃
Frattini, cosocle	C₄	C₂³×C₂₆₃
socle	C₂×C₂₆₃	C₂²×C₄
prime radical	#41×C₂₆₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₆₃ ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30681722, #30682053, #30682058, …
maximal subgroup of	#350×C₂₆₃, #443×C₂₆₃, #444×C₂₆₃, …
maximal normal subgroup of	#350×C₂₆₃, #443×C₂₆₃, #444×C₂₆₃, …
maximal quotient of	#405×C₂₆₃, #408×C₂₆₃, #424×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 38);