C₅×#63727 #13085555

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

Aliases

Hall	C₃²×C₅ ⋊ #100
Sylow	C₃² ⋊ C₅×#100

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

normal subgroups only

This group has 166 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)(12,13,14,17,15,16,18,19);(6,7)(8,11)(9,10)(13,16)(14,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1872);