C₅×#71826 #14282411

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

Aliases

Hall	C₃×C₅ ⋊ #1493
Sylow	C₃ ⋊ C₅×#1493

464 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)(18,19)(23,24);(9,10,12,14)(11,16,15,13)(17,19,22,18)(20,23,21,24);(7,8)(10,13)(11,15)(14,16)(17,18,21,23,22,19,20,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 8109);