Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = C2×D3×#575 (order 768) · Inn(G) = D12 · Out(G) = C25 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #364 |
46 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)(4,6,8,16,10,17,9,7)(5,11,13,15,14,12,18,19);(2,3)(4,5,7,12,9,13,17,19,10,14,16,11,8,18,6,15)Polycyclic presentation:
2^6,3|a^2=c,b^2=d,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #67441, #67443, #67502, … |
| maximal normal subgroup of | #67441, #67443, #67502, … |
| maximal quotient of | #67439, #67440, #67658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 22);