C₅×C₃⋊#1304 #14277352

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₅×C₃⋊#1304
unambiguous semidirect product	C₃⋊(C₅×#1304)

Hall	C₃×C₅ ⋊ #1304
Sylow	C₃ ⋊ C₅×#1304

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

normal subgroups only

This group has 792 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) = 240

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 3050);