C₅×#72133 #14296919

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

Hall	C₃×C₅ ⋊ #1784
Sylow	C₃ ⋊ C₅×#1784

1128 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(6,7,8)(10,12);(13,15,17,23)(14,18,19,21)(16,24,25,22)(20,28,27,26);(7,8)(9,10)(11,12)(13,14,16,20,17,19,25,27)(15,21,22,28,23,18,24,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22617);