C₅²×C₃⋊C₁₆ #11924978

order	1200
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₅²×C₁₆ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₃⋊C₁₆
unambiguous semidirect product	C₃⋊(C₅²×C₁₆)

derived, Sylow	C₃ ⋊ C₅²×C₁₆
Hall	C₃×C₅² ⋊ C₁₆

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 2 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 188);