Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) order 6144 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #418 |
190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(9,14)(10,11)(13,15);(8,10,12,11)(9,13,15,14);(2,3)(4,5,6,7)(8,9)(10,13)(11,14)(12,15)Polycyclic presentation:
2^6,3|a^2=d,b^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^2,c^b=cf,e^c=ef42 conjugacy classes — view the full character table.
| maximal subgroup of | #69643, #69663, #70072, … |
| maximal normal subgroup of | #69643, #69663, #70072, … |
| maximal quotient of | #71554, #71558, #71597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 774);