D₁₄₄ #63358

order	288
isoclinism	isoclinic class of D₁₄₄
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

D₁₄₄

Fitting	C₉×C₁₆ ⋊ C₂
Sylow	C₉ ⋊ D₁₆

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,25)(19,24)(20,23)(21,22)

Polycyclic presentation:

2^5,3^2|b^2=cd,c^2=de,d^2=e,f^3=g^2,b^a=bc,c^a=cd,d^a=de,f^a=f^2g,g^a=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 6);