C₅×#71638 #14281563

order	1920
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₅ ⋊ #1476
Sylow	C₃ ⋊ C₅×#1476

552 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)(17,19,20,24)(18,21,23,22);(17,18)(19,21)(20,23)(22,24);(7,8)(9,10,11,13,12,14,15,16)(17,18,19,21,20,23,24,22)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7261);