Q₃₂×C₂₇₁ #22576034

order	8672
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₇₁ · Schur multiplier (H₂) = C₁

Aliases

Q₃₂×C₂₇₁

	subgroup	G/H
center, socle, prime radical	C₂×C₂₇₁	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₂₇₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₇₁ ◁ C₄×C₂₇₁ ◁ C₈×C₂₇₁ ◁ G

24 conjugacy classes of subgroups.

2981 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8672, 20);