Q₃₂×C₂₆₉ #22575327

order	8608
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₆₉ · Schur multiplier (H₂) = C₁

Aliases

Q₃₂×C₂₆₉

	subgroup	G/H
center, socle, prime radical	C₂×C₂₆₉	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₂₆₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₆₉ ◁ C₄×C₂₆₉ ◁ C₈×C₂₆₉ ◁ G

24 conjugacy classes of subgroups.

2959 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8608, 20);