C₂²×C₁₉×#456 #18066340

order	4864
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂²×C₁₉×#456

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂²×C₁₉×2₋¹⁺⁴	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

4766 conjugacy classes of subgroups.

1216 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 53369);