C₅×#71765 #14305961

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³×C₄

Aliases

Hall	C₃×C₅ ⋊ #1961
Sylow	C₃ ⋊ C₅×#1961

824 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)(13,14,15,16)(18,22)(19,24);(7,8)(9,11,12,10)(17,19,23,18,21,24,20,22);(7,8)(9,10,12,11)(14,16)(17,18)(19,23)(20,24)(21,22)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 31659);