C₁₉×#681 #13095070

order	1520
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₅×C₁₉ ⋊ M₁₆
Sylow	C₅ ⋊ M₁₆×C₁₉

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 760

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,24,22)(26,29)(30,32);(21,22)(23,24)(25,26,27,30,28,29,31,32)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 54);