D₅×D₁₇ #66777

order	340
isoclinism	isoclinic class of D₅×D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

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

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

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 85

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(340, 11);