C₁₇×C₁₉ #66308

order	323
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₉×C₁₆ (order 288) · Inn(G) = C₁ · Out(G) = C₂×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₃
abelian	C₁₇×C₁₉

4 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 323

A minimal faithful permutation representation — 1 generator on 36 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)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(323, 1);