C₂×C₁₉×#322 #14559305

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₁₉×#322

248 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4,5,8,6,7,9,10);(4,7)(8,10)(11,12,13,15,14,16,17,18)

1520 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 180);