C₂²×C₃⋊C₁₆ #5096

order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = C₂×D₃×#87519 (order 4608) · Inn(G) = D₃ · Out(G) = C₂×#87519
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₃⋊C₁₆

C₃ ⋊ C₂²×C₁₆

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 655);