Dic₃×C₄₁ #92445

order	492
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×C₅×D₃×C₈ (order 480) · Inn(G) = D₃ · Out(G) = C₂×C₅×C₈
homology	Abelianization (H₁) = C₄×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₄₁
unambiguous semidirect product	C₃⋊(C₄×C₄₁)

derived, Sylow	C₃ ⋊ C₄×C₄₁
Hall	C₃×C₄₁ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 492

A minimal faithful permutation representation — 2 generators on 48 points:

(2,3)(4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(492, 1);