Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#3003 (order 768) · Inn(G) = C2×D12 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ #444 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,7,8,15,9,16,17,6)(5,10,11,18,13,19,12,14);(4,6,8,7,9,15,17,16)(5,10,12,14,13,19,11,18);(2,3)(4,5)(6,14)(7,10)(8,11)(9,13)(12,17)(15,18)(16,19)Polycyclic presentation:
2^6,3|b^2=e,c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^2,c^b=cf42 conjugacy classes — view the full character table.
| maximal subgroup of | #69090, #69091, #70917, … |
| maximal normal subgroup of | #69090, #69091, #70917, … |
| maximal quotient of | #68076, #68077, #68078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 276);