C₂₉×#170 #11923903

order	1160
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₈×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₅ ⋊ C₈×C₂₉
Hall	C₅×C₂₉ ⋊ C₈

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1160

A minimal faithful permutation representation — 2 generators on 42 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)(31,32,33,34)(35,36,37,39,38,40,41,42);(30,31,32,34,33)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1160, 6);