C₂×C₇×C₂₉ #87962

order	406
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄×C₇ (order 168) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₄₀₆
abelian	C₂×C₇×C₂₉

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 406

A minimal faithful permutation representation — 1 generator on 38 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)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(406, 6);