Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C24×D3×D4 (order 768) · Inn(G) = #67 · Out(G) = C25 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #334 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,5,6,8,7,9,10,11)(13,16)(14,18)(17,19);(2,3)(12,13,14,16,15,17,18,19)Polycyclic presentation:
2^6,3|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bdf,g^a=g^2,d^b=df48 conjugacy classes — view the full character table.
| maximal subgroup of | #68149, #68151, #68154, … |
| maximal normal subgroup of | #68149, #68151, #68154, … |
| maximal quotient of | #67464, #67554, #67567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 39);