C₂²×C₄³×C₁₇ #16891729

order	4352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 33822867456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

C₂²×C₄³×C₁₇

8094 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 5 generators on 33 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26973);