C₅×D₃₅ #66841

order	350
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃₅
unambiguous semidirect product	C₅⋊(C₅×D₇)
unambiguous semidirect product	C₇⋊(C₅×D₅)

	subgroup	G/H
center, hypercenter	C₅	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₅

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 70

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(350, 7);