C₅×#71611 #14300472

order	1920
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

Hall	C₃×C₅ ⋊ #1870
Sylow	C₃ ⋊ C₅×#1870

816 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26170);