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) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #356 |
60 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)(4,6,9,7)(5,10,13,18)(8,16,17,15)(11,19,14,12);(2,3)(4,5,7,11,9,13,6,14)(8,12,15,18,17,19,16,10)Polycyclic presentation:
2^6,3|a^2=c,b^2=f,c^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 | #67463, #67551, #67552, … |
| maximal normal subgroup of | #67463, #67551, #67552, … |
| maximal quotient of | #67635, #67643, #67644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 107);