C₅×#63378 #13083820

order	1440
isoclinism	isoclinic class of Dic₃₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

Hall	C₅×C₉ ⋊ #107
Sylow	C₉ ⋊ C₅×#107

108 conjugacy classes of subgroups.

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

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 137);