order	152
isoclinism	isoclinic class of D₁₉
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₉) (order 2736) · Inn(G) = D₁₉ · Out(G) = D₄×C₉
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×Dic₁₉
unambiguous semidirect product	(C₂×C₁₉)⋊C₄

Splittings

C₁₉ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 152

A minimal faithful permutation representation — 2 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(152, 6);