D₂₃₁ #90765

order	462
isoclinism	isoclinic class of D₂₃₁
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₃₁
unambiguous semidirect product	C₃⋊D₇₇
unambiguous semidirect product	C₇⋊D₃₃
unambiguous semidirect product	C₁₁⋊D₂₁

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₁	C₂
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 231

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)(5,10)(6,9)(7,8)(12,21)(13,20)(14,19)(15,18)(16,17)

Polycyclic presentation:

2,3,7,11|b^a=b^2,c^a=c^6,d^a=d^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(462, 11);