C₃²×C₂²⋊#170 #13086264

order	1440
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₈ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Hall	C₃²×C₅ ⋊ C₂²⋊C₈
Sylow	C₅ ⋊ C₃²×C₂²⋊C₈

300 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3)(7,8,9,11,10)(13,15);(4,5,6)(8,9,10,11)(12,13)(14,15)(16,17,18,20,19,21,22,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2581);