D₁₉₅ #87618

order	390
isoclinism	isoclinic class of D₁₉₅
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₉₅
unambiguous semidirect product	C₃⋊D₆₅
unambiguous semidirect product	C₅⋊D₃₉
unambiguous semidirect product	C₁₃⋊D₁₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₁₃
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 195

A minimal faithful permutation representation — 2 generators on 21 points:

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

Polycyclic presentation:

2,3,5,13|b^a=b^2,c^a=c^4,d^a=d^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(390, 11);