D₁₄₃ #63350

order	286
isoclinism	isoclinic class of D₁₄₃
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₃
unambiguous semidirect product	C₁₁⋊D₁₃
unambiguous semidirect product	C₁₃⋊D₁₁

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃	C₂
LCS	G ▷ C₁₁×C₁₃
UCS	C₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 143

A minimal faithful permutation representation — 2 generators on 24 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

Polycyclic presentation:

2,11,13|b^a=b^10,c^a=c^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(286, 3);