C₅×#63643 #13085063

order	1440
isoclinism	isoclinic class of #3744
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

Hall	C₃²×C₅ ⋊ #103
Sylow	C₃² ⋊ C₅×#103

252 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 118 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)(6,8,9,7)(10,11,12,14,13,15,16,17)(21,22,23);(6,7,9,8)(11,14)(12,16)(15,17)(19,20)(22,23);(18,19,20)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1380);