C₅×Dic₃×C₂₅ #13093721

order	1500
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₂₅ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅×Dic₃×C₂₅
unambiguous semidirect product	C₃⋊(C₄×C₅×C₂₅)

derived, Sylow	C₃ ⋊ C₄×C₅×C₂₅
Hall	C₃×C₅×C₂₅ ⋊ C₄

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1500

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5)(31,32)(33,34)(35,36,37);(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)(31,33,32,34)(36,37)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1500, 22);