C₅×C₃⋊(C₇⋊C₁₆) #13131989

order	1680
isoclinism	isoclinic class of D₂₁
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₃⋊(C₇⋊C₁₆)
unambiguous semidirect product	C₃⋊(C₅×C₇⋊C₁₆)
unambiguous semidirect product	C₇⋊(C₅×C₃⋊C₁₆)

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1680

A minimal faithful permutation representation — 2 generators on 31 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 9);