C₅×#63895 #13087152

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

Aliases

Hall	C₃²×C₅ ⋊ C₂²⋊Q₈
Sylow	C₃² ⋊ C₅×C₂²⋊Q₈

330 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 240

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3469);