Dic₉⋊A₄ #88618

order	432
isoclinism	isoclinic class of D₉⋊A₄
automorphism	Aut(G) = C₂×A₄×AGL(1,ℤ/9) (order 1296) · Inn(G) = D₉⋊A₄ · Out(G) = C₂×C₃
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	Dic₉⋊A₄
unambiguous semidirect product	(C₉⋊A₄)⋊C₄

C₂²×C₉ ⋊ C₃×C₄

61 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 17 points:

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

Polycyclic presentation:

2,3,2^3,3^2|a^2=c,f^3=g^2,f^a=f^2g,g^a=g^2,d^b=de,e^b=d,f^b=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 265);