C₁₇×D₉ #64556

order	306
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₁₆×AGL(1,ℤ/9) (order 864) · Inn(G) = D₉ · Out(G) = C₃×C₁₆
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₉
unambiguous semidirect product	C₉⋊(C₂×C₁₇)

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

	subgroup	G/H
center, hypercenter	C₁₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₇
Frattini	C₃	D₃×C₁₇
Fitting	C₉×C₁₇	C₂
socle	C₃×C₁₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₇

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(306, 1);