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C₂×C₂²⋊C₄×C₂₆₃ #22554346

order	8416
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₆₃ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₂²⋊C₄×C₂₆₃

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₆₃	C₂²
commutator	C₂	C₂²×C₄×C₂₆₃
Frattini, cosocle	C₂²	C₂³×C₂₆₃
prime radical	C₂⁴×C₂₆₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₆₃ ◁ G

132 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	#30681662, #30681704, #30681705, …
maximal subgroup of	#323×C₂₆₃, #342×C₂₆₃, C₄×C₂²⋊C₄×C₂₆₃, …
maximal normal subgroup of	#323×C₂₆₃, #342×C₂₆₃, C₄×C₂²⋊C₄×C₂₆₃, …
maximal quotient of	C₂×#95×C₂₆₃, C₄×C₂²⋊C₄×C₂₆₃, #379×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 22);