D₅×D₁₃ #63123

order	260
isoclinism	isoclinic class of D₅×D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

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

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

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 65

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(260, 11);