#509×C₈₃ #19127342

order	5312
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, socle	C₂×C₈₃	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂³×C₈₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₃ ◁ C₂×C₄×C₈₃ ◁ C₂×C₈×C₈₃ ◁ G

90 conjugacy classes of subgroups.

1328 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5312, 190);