C₃×#4015 #91586

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ C₄⋊Q₈
Sylow	C₅ ⋊ C₃×C₄⋊Q₈

136 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 662);