C₉⋊SL(2,ℤ/4) #88607

order	432
isoclinism	isoclinic class of C₉⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

unambiguous semidirect product	C₉⋊SL(2,ℤ/4)
unambiguous semidirect product	A₄⋊Dic₉

C₉×A₄ ⋊ C₄

81 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 17 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 254);