C₅²×C₁₉ #90908

order	475
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₅²×C₁₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 475

A minimal faithful permutation representation — 2 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(475, 2);