Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#33551 (order 1536) · Inn(G) = #834 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #354 |
70 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)(4,6,8,13)(5,9,11,18)(7,16,17,14)(10,19,15,12);(2,3)(4,5)(6,12,13,19)(7,15,17,10)(8,11)(9,14)(16,18)Polycyclic presentation:
2^6,3|a^2=c,b^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,c^b=ce,d^b=df,d^c=df27 conjugacy classes — view the full character table.
| maximal subgroup of | #67460, #67547, #67548, … |
| maximal normal subgroup of | #67460, #67547, #67548, … |
| maximal quotient of | #67632, #67641, #67643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 100);