C₅×#67630 #14277153

order	1920
isoclinism	isoclinic class of #4537
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ #1295
Sylow	C₃ ⋊ C₅×#1295

360 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 1920

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2851);