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SD₁₆×C₅₂₃ #22552609

order	8368
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅₂₃ · Schur multiplier (H₂) = C₁

Aliases

SD₁₆×C₅₂₃

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₂₃	D₄
commutator, Frattini	C₄	C₂²×C₅₂₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₂₃ ◁ C₄×C₅₂₃ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3661 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	SD₁₆×D₅₂₃, #30660394, #30660400, …
maximal subgroup of	C₂×SD₁₆×C₅₂₃, #135×C₅₂₃, AGL(1,ℤ/8)×C₅₂₃, …
maximal normal subgroup of	C₂×SD₁₆×C₅₂₃, #135×C₅₂₃, AGL(1,ℤ/8)×C₅₂₃, …
maximal quotient of	#102×C₅₂₃, #103×C₅₂₃, #106×C₅₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8368, 8);