C₅×C₈×C₂₉ #11923901

order	1160
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₇ (order 448) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₆₀
abelian	C₅×C₈×C₂₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1160

A minimal faithful permutation representation — 1 generator on 42 points:

(1,2,3,4,5,6,7,8)(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)

1160 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1160, 4);