C₅×#67644 #14279133

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ #1394
Sylow	C₃ ⋊ C₅×#1394

344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

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

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

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4831);