C₂³×C₃×C₄₁ #11758332

order	984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 13440
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂³×C₃×C₄₁
multiplicative	(ℤ/1743)ˣ, (ℤ/2324)ˣ, (ℤ/2988)ˣ, (ℤ/3486)ˣ

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 984

A minimal faithful permutation representation — 3 generators on 50 points:

(1,2)(7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(3,4);(5,6)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(984, 46);