C₉⋊(C₄²⋊C₃) #88453

order	432
isoclinism	isoclinic class of C₉⋊(C₄²⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₄

Aliases

C₉⋊(C₄²⋊C₃)

Fitting	C₄²×C₉ ⋊ C₃
Sylow	C₄² ⋊ 3₋¹⁺²

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 21 points:

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

Polycyclic presentation:

3^3,2^4|b^3=c,d^2=fg,e^2=f,b^a=bc,d^a=e,e^a=deg,f^a=g,g^a=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 100);