Dic₈₅ #66769

order	340
isoclinism	isoclinic class of D₈₅
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

Dic₈₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₅
commutator, hypocenter	C₅×C₁₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 340

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26);(1,3,2,4)(6,9)(7,8)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

Polycyclic presentation:

2^2,5,17|a^2=b,c^a=c^4,d^a=d^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(340, 3);