order	204
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂²×AGL(1,𝔽₁₇) (order 1088) · Inn(G) = D₁₇ · Out(G) = C₂²×C₈
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₁₇

Splittings

derived, Sylow	C₁₇ ⋊ C₃×C₄
Hall	C₃×C₁₇ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 204

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(4,5)(6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24);(4,6,5,7)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(204, 2);