(C₂×D₉)⋊C₄ #3671

order	144
isoclinism	isoclinic class of Dic₁₈
automorphism	Aut(G) = C₂⁴×AGL(1,ℤ/9) (order 864) · Inn(G) = C₂×D₉ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

(C₂×D₉)⋊C₄

Fitting	C₂×C₄×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂²⋊C₄

51 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 17 points:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 14);