C₅×#63741 #13085569

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₃²×C₅ ⋊ #104
Sylow	C₃² ⋊ C₅×#104

158 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1886);