C₅×#64153 #13088124

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

Aliases

Hall	C₃²×C₅ ⋊ C₄⋊Q₈
Sylow	C₃² ⋊ C₅×C₄⋊Q₈

408 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 1440

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)(16,17,19,21)(18,22,23,20);(7,8)(10,11)(12,13,14,15)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4441);