Dic₆₅ #63115

order	260
isoclinism	isoclinic class of D₆₅
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

Dic₆₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₅
commutator, hypocenter	C₅×C₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₃	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 260

A minimal faithful permutation representation — 2 generators on 22 points:

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

Polycyclic presentation:

2^2,5,13|a^2=b,c^a=c^4,d^a=d^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(260, 3);