C₉×D₅⋊M₁₆ #13085228

order	1440
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₉×D₅⋊M₁₆
unambiguous semidirect product	D₅⋊(C₉×M₁₆)

Hall	C₅×C₉ ⋊ C₂×M₁₆
Sylow	C₅ ⋊ C₂×C₉×M₁₆

204 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

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

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 360

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1545);