Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×#62817 (order 3072) · Inn(G) = C22×D3 · Out(G) = C27 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #432 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(13,16)(17,19);(5,8)(9,11);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^6,3|a^2=d,c^2=e,d^2=f,b^a=be,c^a=cf,g^a=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #67615, #67621, #67633, … |
| maximal normal subgroup of | #67615, #67621, #67633, … |
| maximal quotient of | #69389, #69391, #69392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 485);