C₅×#68652 #14296292

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₅ ⋊ #1770
Sylow	C₃ ⋊ C₅×#1770

544 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1920

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21990);