order	208
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₃×C₄×AGL(1,ℤ/8) (order 384) · Inn(G) = D₄ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

C₁₃×D₈

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ G

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 25);