C₂×C₃×#689 #91660

order	480
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ C₂×C₃×Q₁₆

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 480

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 736);