C₉×D₁₇ #64557

order	306
isoclinism	isoclinic class of D₁₇
automorphism	Aut(G) = C₂×C₃×AGL(1,𝔽₁₇) (order 1632) · Inn(G) = D₁₇ · Out(G) = C₂×C₃×C₈
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₉)

Fitting, Hall	C₉×C₁₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₉

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 153

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,4,3,5,7,6,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);(10,11,13,15,17,19,21,23,25,26,24,22,20,18,16,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(306, 2);