C₅×#70528 #14297587

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₅ ⋊ #1801
Sylow	C₃ ⋊ C₅×#1801

544 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 960

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23285);