C₄×#261 #6119

order	208
isoclinism	isoclinic class of #261
automorphism	Aut(G) = D₄×AGL(1,𝔽₁₃) (order 1248) · Inn(G) = #261 · Out(G) = C₃×D₄
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

Fitting	C₄×C₁₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄²

30 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 30);