C₅×#63981 #13087250

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

Hall	C₃²×C₅ ⋊ #120
Sylow	C₃² ⋊ C₅×#120

654 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 112 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 — 3 generators on 19 points:

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

maximal subgroup of	D₅×#63981
maximal normal subgroup of	D₅×#63981

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3567);