order	102
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = D₃×C₁₆ (order 96) · Inn(G) = D₃ · Out(G) = C₁₆
holomorph	G ⋊ Aut(G) = D₃²×AGL(1,𝔽₁₇)
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₇
unambiguous semidirect product	C₃⋊(C₂×C₁₇)

Splittings

Fitting, socle, Hall	C₃×C₁₇ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₇

	subgroup	G/H
center, hypercenter	C₁₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₇

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 51

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(102, 1);