C₉⋊(C₂²⋊A₄) #88905

order	432
isoclinism	isoclinic class of C₉⋊(C₂²⋊A₄)
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₂⁴

Aliases

C₉⋊(C₂²⋊A₄)

Fitting	C₂⁴×C₉ ⋊ C₃
Sylow	C₂⁴ ⋊ 3₋¹⁺²

116 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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 552);