C₉×#4070 #13084400

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₉ ⋊ C₂²⋊Q₈
Sylow	C₅ ⋊ C₉×C₂²⋊Q₈

222 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 111 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 — 3 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 717);