C₅×#67683 #14277185

order	1920
isoclinism	isoclinic class of #4537
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₅ ⋊ #1297
Sylow	C₃ ⋊ C₅×#1297

492 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 480

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2883);