C₅×#63431 #13084431

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₉ ⋊ C₄⋊Q₈
Sylow	C₉ ⋊ C₅×C₄⋊Q₈

204 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 1440

A minimal faithful permutation representation — 3 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 748);