#1088⋊C₂ #6250

order	216
isoclinism	isoclinic class of #1088⋊C₂
automorphism	Aut(G) = #6249⋊C₂ (order 432) · Inn(G) = G · Out(G) = C₂
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	#1088⋊C₂
unambiguous semidirect product	(((C₃⋊D₃)⋊C₃)⋊C₂)⋊C₂

44 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:

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

Polycyclic presentation:

2^3,3^3|b^a=bc,d^a=d^2,f^a=f^2,d^b=e,e^b=d,f^b=f^2,d^c=d^2,e^c=e^2,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 87);