Dic₃⋊Dic₉ #88443

order	432
isoclinism	isoclinic class of #6189
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

94 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 20 points:

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

Polycyclic presentation:

2^4,3^3|a^2=d,b^2=c,e^3=g^2,b^a=bd,f^a=f^2,e^b=e^2g,g^b=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 90);