C₉×#3944 #13083773

order	1440
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₉ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₅×C₉ ⋊ M₃₂
Sylow	C₅ ⋊ C₉×M₃₂

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 720

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9)(10,11,13,14,12)(16,20)(21,26)(22,27)(28,30);(11,12)(13,14)(15,16,17,21,18,22,23,28,19,20,24,26,25,27,29,30)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 90);