C₅×#67792 #14279435

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

Aliases

Hall	C₃×C₅ ⋊ #1408
Sylow	C₃ ⋊ C₅×#1408

240 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5133);