order	156
isoclinism	isoclinic class of D₁₃
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₃) (order 624) · Inn(G) = D₁₃ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₁₃

Splittings

derived, Sylow	C₁₃ ⋊ C₃×C₄
Hall	C₃×C₁₃ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(156, 4);