D₉₅ #4439

order	190
isoclinism	isoclinic class of D₉₅
automorphism	Aut(G) = AGL(1,𝔽₅)×AGL(1,𝔽₁₉) (order 6840) · Inn(G) = G · Out(G) = C₄×C₉
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₅
unambiguous semidirect product	C₅⋊D₁₉
unambiguous semidirect product	C₁₉⋊D₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 95

A minimal faithful permutation representation — 2 generators on 24 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);(2,5)(3,4)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)

Polycyclic presentation:

2,5,19|b^a=b^4,c^a=c^18

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(190, 3);