C₂×C₈×C₂₉ #90790

order	464
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄×C₇×D₄ (order 448) · Inn(G) = C₁ · Out(G) = C₂×C₄×C₇×D₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₈×C₂₉
multiplicative	(ℤ/699)ˣ, (ℤ/932)ˣ, (ℤ/1398)ˣ

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,3,4,5,6,7,8)(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);(9,10)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 23);