order	480
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₄⋊(C₃⋊C₈)
unambiguous semidirect product	C₄⋊(C₅×C₃⋊C₈)

Splittings

Hall	C₃×C₅ ⋊ C₄⋊C₈
Sylow	C₃ ⋊ C₅×C₄⋊C₈

76 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 123);