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#108×C₂₆₃ #22554339

order	8416
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₆₃ · Schur multiplier (H₂) = C₁

Aliases

#108×C₂₆₃

Subgroups

	subgroup	G/H
center	C₄×C₂₆₃	D₄
commutator	C₄	C₂×C₄×C₂₆₃
Frattini, cosocle	C₂×C₄	C₂²×C₂₆₃
socle	C₂×C₂₆₃	C₄⋊C₄
prime radical	C₂²×C₂₆₃	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₆₃ ◁ C₂×C₄×C₂₆₃ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3682 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30681744, #30681750, #30681753, …
maximal subgroup of	#359×C₂₆₃, #361×C₂₆₃, #362×C₂₆₃, …
maximal normal subgroup of	#359×C₂₆₃, #361×C₂₆₃, #362×C₂₆₃, …
maximal quotient of	#334×C₂₆₃, #335×C₂₆₃, #341×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 15);