C₅×#71839 #14307409

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₅ ⋊ #1994
Sylow	C₃ ⋊ C₅×#1994

568 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 480

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 33107);