D₂₇₃ #10587734

order	546
isoclinism	isoclinic class of D₂₇₃
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₇₃
unambiguous semidirect product	C₃⋊D₉₁
unambiguous semidirect product	C₇⋊D₃₉
unambiguous semidirect product	C₁₃⋊D₂₁

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃	C₂
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 273

A minimal faithful permutation representation — 2 generators on 23 points:

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

Polycyclic presentation:

2,3,7,13|b^a=b^2,c^a=c^6,d^a=d^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(546, 23);