C₄²×C₁₆×C₁₇ #16870281

order	4352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3145728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

C₄²×C₁₆×C₁₇

558 conjugacy classes of subgroups.

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 41 points:

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

4352 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5525);