order	228
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂²×D₃×C₉ (order 216) · Inn(G) = D₃ · Out(G) = C₂²×C₉
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₉
unambiguous semidirect product	C₃⋊(C₄×C₁₉)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 228

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26);(1,3,2,4)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(228, 3);