C₂₅×C₃⋊C₁₆ #11924791

order	1200
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₁₆×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×C₃⋊C₁₆
unambiguous semidirect product	C₃⋊(C₁₆×C₂₅)

derived, Sylow	C₃ ⋊ C₁₆×C₂₅
Hall	C₃×C₂₅ ⋊ C₁₆

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1200

A minimal faithful permutation representation — 2 generators on 44 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)(27,28)(29,30,31,34,32,35,37,40,33,36,38,41,39,42,43,44);(26,27,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 1);