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C₄×Q₈×C₂₆₃ #22554350

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

Aliases

C₄×Q₈×C₂₆₃

Subgroups

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

70 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	Q₈⋊(C₂₆₃⋊C₈), C₄×#16862363, C₄×#16862366, …
maximal subgroup of	Q₈⋊C₈×C₂₆₃, C₄×SD₁₆×C₂₆₃, C₄×Q₁₆×C₂₆₃, …
maximal normal subgroup of	Q₈⋊C₈×C₂₆₃, C₄×SD₁₆×C₂₆₃, C₄×Q₁₆×C₂₆₃, …
maximal quotient of	C₄×C₄⋊C₄×C₂₆₃, #387×C₂₆₃, #389×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 26);