C₅×#72142 #14297134

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

Hall	C₃×C₅ ⋊ #1790
Sylow	C₃ ⋊ C₅×#1790

1340 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.

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

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22832);