C₁₇×#1039 #13133333

order	1700
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇ · Schur multiplier (H₂) = C₅

Aliases

derived, Sylow	C₅² ⋊ C₄×C₁₇
Hall	C₅²×C₁₇ ⋊ C₄

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1700

A minimal faithful permutation representation — 3 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(23,24)(25,26)(28,29)(30,31);(27,28,30,31,29);(22,23,25,26,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1700, 19);