C₅×#63659 #13085075

order	1440
isoclinism	isoclinic class of #3753
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Hall	C₃²×C₅ ⋊ #102
Sylow	C₃² ⋊ C₅×#102

300 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 138 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)(11,14)(12,17)(15,16)(21,22,23);(6,7,8,9)(10,11)(12,14)(13,16)(15,17)(19,20)(22,23);(18,19,20)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1392);