C₃²×#4081 #13087859

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

Hall	C₃²×C₅ ⋊ #123
Sylow	C₅ ⋊ C₃²×#123

468 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 198 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) = 720

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4176);