C₉×C₄₁ #67301

order	369
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₅×C₈ (order 240) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₅×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₆₉
abelian	C₉×C₄₁

6 conjugacy classes of subgroups.

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 369

A minimal faithful permutation representation — 1 generator on 50 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(369, 1);