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#103×C₂₆₃ #22554334

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

Aliases

#103×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

42 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	#103×D₂₆₃, #30681933, #30681938, …
maximal subgroup of	C₂×#103×C₂₆₃, #416×C₂₆₃, #417×C₂₆₃, …
maximal normal subgroup of	C₂×#103×C₂₆₃, #416×C₂₆₃, #417×C₂₆₃, …
maximal quotient of	Q₈⋊C₈×C₂₆₃, #328×C₂₆₃, #332×C₂₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8416, 10);