C₉×#3964 #13083794

order	1440
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₉ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₉ ⋊ #102
Sylow	C₅ ⋊ C₉×#102

150 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

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

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 111);