Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C22×D3×#41 (order 384) · Inn(G) = #67 · Out(G) = C24 |
| 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)(4,6,7,14,9,15,13,18,10,16,12,19,8,17,5,11);(2,3)(4,5,8,12,10,13,9,7)(6,14,15,18,16,19,17,11)Polycyclic presentation:
2^6,3|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,g^a=g^2,d^b=df48 conjugacy classes — view the full character table.
| maximal subgroup of | #69088, #69089, #69114, … |
| maximal normal subgroup of | #69088, #69089, #69114, … |
| maximal quotient of | #67554, #67555, #67810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 70);