Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#3109 (order 768) · Inn(G) = #809 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×#106 ⋊ C2 |
| Sylow | C3 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(5,9,10,18)(6,13)(7,14)(11,17,19,12)(15,16);(2,3)(4,5)(6,9)(7,17)(8,10)(11,15)(12,14)(13,19)(16,18)Polycyclic presentation:
2^6,3|b^2=c,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^2,d^b=def,e^b=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#360, #69251, #69252, … |
| maximal normal subgroup of | D3×#360, #69251, #69252, … |
| maximal quotient of | #67465, #67466, #67467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 47);