order	102
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂×AGL(1,𝔽₁₇) (order 544) · Inn(G) = D₁₇ · Out(G) = C₂×C₈
holomorph	G ⋊ Aut(G) = D₃×#72213403
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₃)

Splittings

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

	subgroup	G/H
center, hypercenter	C₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(102, 2);