order	184
isoclinism	isoclinic class of D₂₃
automorphism	Aut(G) = C₂²×AGL(1,𝔽₂₃) (order 2024) · Inn(G) = D₂₃ · Out(G) = C₂²×C₁₁
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₂₃

Splittings

Fitting	C₄×C₂₃ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂×C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 92

A minimal faithful permutation representation — 2 generators on 27 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,26,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(184, 4);