D₂₃ #196

order	46
isoclinism	isoclinic class of D₂₃
automorphism	Aut(G) = AGL(1,𝔽₂₃) (order 506) · Inn(G) = G · Out(G) = C₁₁
holomorph	G ⋊ Aut(G) = #26042787⋊C₂
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₂₃
unambiguous semidirect product	C₂₃⋊C₂

C₂₃ ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁

4 conjugacy classes of subgroups.

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

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

Polycyclic presentation:

2,23|b^a=b^22

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(46, 1);