Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C24×C4×D3 (order 384) · Inn(G) = C2×D3 · Out(G) = C23×C4 |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic3⋊C16 |
| Sylow | C3 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(5,7)(8,9,10,13,11,14,16,19,12,15,17,20,18,21,22,23);(2,3)(4,5,6,7)Polycyclic presentation:
2^6,3|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bd,g^a=g^272 conjugacy classes — view the full character table.
| maximal subgroup of | C16×Dic6, #69048, #69052, … |
| maximal normal subgroup of | C16×Dic6, #69048, #69052, … |
| maximal quotient of | #67554, #67555, Dic3⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 60);