C₂×C₅×C₄₁ #88016

order	410
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₄×C₅×C₈ (order 160) · Inn(G) = C₁ · Out(G) = C₄×C₅×C₈
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₁₀
abelian	C₂×C₅×C₄₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 410

A minimal faithful permutation representation — 1 generator on 48 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)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(410, 6);