C₅×#869 #91672

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ C₄⋊Q₈
Sylow	C₃ ⋊ C₅×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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 748);