C₇×D₃₅ #92441

order	490
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

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

	subgroup	G/H
center, hypercenter	C₇	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₇

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 70

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(490, 8);