(C₃⋊D₉)⋊C₈ #88412

order	432
isoclinism	isoclinic class of D₃×D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

(C₃⋊D₉)⋊C₈

C₃×C₉ ⋊ C₂×C₈

82 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 20 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 59);