C₂×D₈₅ #66780

order	340
isoclinism	isoclinic class of D₈₅
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₇₀
direct product	C₂×D₈₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₇
unambiguous semidirect product	(C₂×C₁₇)⋊D₅

	subgroup	G/H
center, hypercenter	C₂	D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 170

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(340, 14);