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C₂²⋊C₈×C₂₆₃ #22554329

order	8416
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₂₆₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₈×C₂₆₃
unambiguous semidirect product	C₂²⋊(C₈×C₂₆₃)

Subgroups

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

50 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	#30681661, #30681663, #30681673, …
maximal subgroup of	#323×C₂₆₃, #324×C₂₆₃, #327×C₂₆₃, …
maximal normal subgroup of	#323×C₂₆₃, #324×C₂₆₃, #327×C₂₆₃, …
maximal quotient of	#323×C₂₆₃, #324×C₂₆₃, D₄⋊C₈×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 5);