C₈₉×SD₁₂₈ #26015904

order	11392
nilpotency class	6
isoclinism	isoclinic class of D₆₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

C₈₉×SD₁₂₈

	subgroup	G/H
center, socle	C₂×C₈₉	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₈₉
prime radical	D₃₂×C₈₉	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₄×C₈₉ ◁ C₈×C₈₉ ◁ C₁₆×C₈₉ ◁ C₃₂×C₈₉ ◁ G

38 conjugacy classes of subgroups.

3115 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 162);