C₅×#63937 #13087209

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃²×C₅ ⋊ AGL(1,ℤ/8)
Sylow	C₃² ⋊ C₅×AGL(1,ℤ/8)

326 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 76 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)(7,12)(8,13)(9,11)(14,15,16)(17,18,19);(6,8,10,12)(7,11,13,9)(15,16);(6,7)(8,11)(9,12)(10,13)(18,19)

maximal subgroup of	D₅×#63937, C₅×#10595100, #72230425
maximal normal subgroup of	D₅×#63937, C₅×#10595100, #72230425

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3526);