C₃×C₄⋊#168 #91006

order	480
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊#168
unambiguous semidirect product	C₄⋊(C₃×#168)

Hall	C₃×C₅ ⋊ C₄⋊C₈
Sylow	C₅ ⋊ C₃×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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 82);