C₃²×#4023 #13087802

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃×C₄

Aliases

Hall	C₃²×C₅ ⋊ #117
Sylow	C₅ ⋊ C₃²×#117

456 conjugacy classes of subgroups; only the 246 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 246 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)(12,13,14,15)(18,22)(20,23);(4,5,6)(16,18)(17,20)(19,22)(21,23);(8,9)(10,11)(16,17,19,21)(18,20,22,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4119);