C₅×#63955 #13087225

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃²×C₅ ⋊ #117
Sylow	C₃² ⋊ C₅×#117

338 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 136 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)(11,15)(14,17)(18,19,20)(21,22,23);(10,12,13,16)(11,14,15,17)(19,20);(6,7,8,9)(10,11)(12,14)(13,15)(16,17)(22,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3542);