Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#394058 (order 3072) · Inn(G) = C22×D3 · Out(G) = #2403 |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(8,9,10,13,11,12,14,15);(4,5,6,7)(9,12)(13,15);(2,3)(9,12)(13,15)Polycyclic presentation:
2^6,3|b^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^2,c^b=cf60 conjugacy classes — view the full character table.
| maximal subgroup of | #68341, #68342, #68343, … |
| maximal normal subgroup of | #68341, #68342, #68343, … |
| maximal quotient of | #68067, #68070, #68072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 266);