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.
| Fitting | C3×#117 ⋊ C2 |
| 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)(4,5,6,7)(8,9)(10,15)(11,13)(12,14);(9,13)(12,15);(2,3)(9,12)(10,14)(13,15)Polycyclic presentation:
2^6,3|c^2=d,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 | #68704, #68706, #68713, … |
| maximal normal subgroup of | #68704, #68706, #68713, … |
| maximal quotient of | #69432, #69444, #69474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 560);