D₃×#125 #5687

order	192
automorphism	Aut(G) order 6144
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₃×#125 ⋊ C₂
Sylow	C₃ ⋊ C₂×#125

226 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1246);