D₂₅₅ #92802

order	510
isoclinism	isoclinic class of D₂₅₅
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₅₅
unambiguous semidirect product	C₃⋊D₈₅
unambiguous semidirect product	C₅⋊D₅₁
unambiguous semidirect product	C₁₇⋊D₁₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₇	C₂
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 255

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25);(2,3)(5,8)(6,7)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)

Polycyclic presentation:

2,3,5,17|b^a=b^2,c^a=c^4,d^a=d^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(510, 7);