C₁₇×#687 #13062696

order	1360
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₅×C₁₇ ⋊ SD₁₆
Sylow	C₅ ⋊ SD₁₆×C₁₇

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 680

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,22,20)(24,27)(25,30)(28,29);(19,20)(21,22)(23,24,26,29)(25,27,30,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 64);