C₉×#4003 #13083965

order	1440
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₉ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₉ ⋊ C₂²⋊C₈
Sylow	C₅ ⋊ C₉×C₂²⋊C₈

150 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 66 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)(10,11,12,14,13)(16,18)(19,21,23,22)(20,24,26,25);(11,12,13,14)(15,16)(17,18)(19,20,22,25,23,26,21,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 282);