C₂₉×#214 #13063550

order	1392
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃×C₂₉ ⋊ SD₁₆
Sylow	C₃ ⋊ SD₁₆×C₂₉

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 696

A minimal faithful permutation representation — 2 generators on 40 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)(34,37)(35,40)(38,39);(31,32)(33,34,36,39)(35,37,40,38)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 61);