order	92
isoclinism	isoclinic class of D₂₃
automorphism	Aut(G) = C₂×AGL(1,𝔽₂₃) (order 1012) · Inn(G) = D₂₃ · Out(G) = C₂×C₁₁
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₄₆
direct product	C₂×D₂₃
unambiguous semidirect product	C₂₃⋊C₂²
unambiguous semidirect product	(C₂×C₂₃)⋊C₂

Splittings

Fitting, socle	C₂×C₂₃ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₂	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂

10 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 46

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25);(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(92, 3);