C₂²⋊D₁₃ #1062

order	104
isoclinism	isoclinic class of Dic₂₆
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₃) (order 624) · Inn(G) = C₂×D₁₃ · Out(G) = C₃×C₄
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

C₂²⋊D₁₃

Fitting	C₂²×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ D₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 52

A minimal faithful permutation representation — 2 generators on 17 points:

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

Polycyclic presentation:

2^3,13|b^a=bc,d^a=d^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(104, 8);