Dic₁₃⋊C₉ #90826

order	468
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	Aut(G) = C₂×C₃×AGL(1,𝔽₁₃) (order 936) · Inn(G) = D₁₃⋊C₃ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

Dic₁₃⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₃	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 468

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

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

Polycyclic presentation:

2,3,2,3,13|a^2=c,b^3=d,e^a=e^12,e^b=e^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 1);