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#117×C₂₆₃ #22554348

order	8416
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₆₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₂₆₃

Subgroups

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

76 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	#30681694, #30681697, #30681708, …
maximal subgroup of	H(3,ℤ/4)×C₂₆₃, #339×C₂₆₃, #344×C₂₆₃, …
maximal normal subgroup of	H(3,ℤ/4)×C₂₆₃, #339×C₂₆₃, #344×C₂₆₃, …
maximal quotient of	#376×C₂₆₃, C₄×C₂²⋊C₄×C₂₆₃, C₄×C₄⋊C₄×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 24);