order	228
isoclinism	isoclinic class of D₁₉
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₉) (order 1368) · Inn(G) = D₁₉ · Out(G) = C₂²×C₉
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₁₉

Splittings

derived, Sylow	C₁₉ ⋊ C₃×C₄
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);(4,6,5,7)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(228, 4);