C₅×#71670 #14302044

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

Hall	C₃×C₅ ⋊ #1898
Sylow	C₃ ⋊ C₅×#1898

1196 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2,3,4,5)(6,7,8)(10,12);(7,8)(13,15)(14,17,18,20)(16,19);(7,8)(9,10)(11,12)(13,14)(15,17,19,20)(16,18)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27742);