C₅×#64087 #13088061

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²×C₃

Aliases

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

444 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 158 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 — 3 generators on 23 points:

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

270 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4378);