C₂×D₆₅ #63126

order	260
isoclinism	isoclinic class of D₆₅
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₃₀
direct product	C₂×D₆₅
unambiguous semidirect product	(C₂×C₅)⋊D₁₃
unambiguous semidirect product	(C₂×C₁₃)⋊D₅

	subgroup	G/H
center, hypercenter	C₂	D₆₅
commutator, cosocle, hypocenter	C₅×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 130

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(260, 14);