C₅×#69674 #14304495

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

Aliases

Hall	C₃×C₅ ⋊ #1933
Sylow	C₃ ⋊ C₅×#1933

512 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)(6,7)(14,16)(17,19,20,24,21,18,23,22);(7,8)(9,11,12,10)(17,18,20,22,21,19,23,24);(7,8)(9,10,12,11)(13,14)(15,16)(18,22)(19,24)(20,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30193);