Q₈×C₁₉×#135 #18067316

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂⁸

Aliases

Q₈×C₁₉×#135

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂³×D₄
prime radical	C₂×C₁₉×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

1786 conjugacy classes of subgroups.

1330 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 54345);