C₄²×C₅×C₁₉ #13095096

order	1520
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

C₄²×C₅×C₁₉

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1520

A minimal faithful permutation representation — 2 generators on 32 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 80);