(C₃⋊D₃)⋊C₉ #4168

order	162
isoclinism	isoclinic class of (C₃⋊D₃)⋊C₃
automorphism	Aut(G) = C₃×((C₃⋊D₃)⋊C₃)⋊C₂ (order 324) · Inn(G) = (C₃⋊D₃)⋊C₃ · Out(G) = C₂×C₃
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₃

Aliases

(C₃⋊D₃)⋊C₉

Fitting, Sylow	C₃²⋊C₉ ⋊ C₂
derived	C₃² ⋊ C₂×C₉

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 18

A minimal faithful permutation representation — 2 generators on 18 points:

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

Polycyclic presentation:

2,3^4|b^3=c,d^a=d^2,e^a=e^2,d^b=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(162, 4);