Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×B(4,𝔽2) (order 768) · Inn(G) = #806 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #352 |
68 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)(4,6,7,13,8,15,16,14)(5,9,10,17,11,18,19,12);(2,3)(4,5,8,11)(6,12,15,17)(7,10,16,19)(9,13,18,14)Polycyclic presentation:
2^6,3|a^2=f,b^2=c,c^2=f,b^a=bd,c^a=ce,g^a=g^2,d^b=de,e^b=ef,d^c=df24 conjugacy classes — view the full character table.
| maximal subgroup of | #69132, #69133, #69135, … |
| maximal normal subgroup of | #69132, #69133, #69135, … |
| maximal quotient of | #67445, #67446, #67450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 35);