order	152
isoclinism	isoclinic class of D₁₉
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₉) (order 1368) · Inn(G) = D₁₉ · Out(G) = C₂²×C₉
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₁₉

Splittings

Fitting	C₄×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 76

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(152, 4);