C₅×#63392 #13083835

order	1440
isoclinism	isoclinic class of #3672
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₉ ⋊ #102
Sylow	C₉ ⋊ C₅×#102

150 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5)(6,7,10,12,14,13,8,11,9)(20,23)(21,26)(24,25);(7,9)(8,12)(10,11)(13,14)(15,16,17,18)(19,20)(21,23)(22,25)(24,26)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 152);