Dic₃×C₃₇ #89219

order	444
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×C₄×D₃×C₉ (order 432) · Inn(G) = D₃ · Out(G) = C₂×C₄×C₉
homology	Abelianization (H₁) = C₄×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₃₇
unambiguous semidirect product	C₃⋊(C₄×C₃₇)

derived, Sylow	C₃ ⋊ C₄×C₃₇
Hall	C₃×C₃₇ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 444

A minimal faithful permutation representation — 2 generators on 44 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);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 3);