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#106×C₂₆₃ #22554337

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

Aliases

#106×C₂₆₃

Subgroups

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

36 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	#30681747, #30681760, #106×D₂₆₃, …
maximal subgroup of	#360×C₂₆₃, #365×C₂₆₃, C₂×#106×C₂₆₃, …
maximal normal subgroup of	#360×C₂₆₃, #365×C₂₆₃, C₂×#106×C₂₆₃, …
maximal quotient of	#334×C₂₆₃, #340×C₂₆₃, #365×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 13);