C₃²×#3967 #13084954

order	1440
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

Hall	C₃²×C₅ ⋊ #103
Sylow	C₅ ⋊ C₃²×#103

252 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 1440

A minimal faithful permutation representation — 2 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1271);