C₅⋊D₃₅ #66843

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

Aliases

unambiguous semidirect product	C₅⋊D₃₅
unambiguous semidirect product	C₇⋊(C₅⋊D₅)

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

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 175

A minimal faithful permutation representation — 3 generators on 17 points:

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

Polycyclic presentation:

2,5^2,7|b^a=b^4,c^a=c^4,d^a=d^6

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(350, 9);