D₃×#126 #5703

order	192
automorphism	Aut(G) order 4608
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₃×#126 ⋊ C₂
Sylow	C₃ ⋊ C₂×#126

246 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1262);