C₅×#64283 #13089164

order	1440
isoclinism	isoclinic class of #3788
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Hall	C₃²×C₅ ⋊ C₂×M₁₆
Sylow	C₃² ⋊ C₂×C₅×M₁₆

244 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 72 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)(6,8,11)(7,10,9)(13,18)(17,19);(12,14,16,15)(13,17,18,19);(6,7)(8,10,11,9)(12,13,15,19,16,18,14,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5481);