Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C2×D3×B(4,𝔽2) (order 768) · Inn(G) = #806 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 11 points:
(1,2,3)(4,5)(6,10,11,8)(7,9);(2,3)(5,8)(9,10)Polycyclic presentation:
2^6,3|b^2=c,b^a=bd,c^a=ce,g^a=g^2,d^b=de,e^b=ef,d^c=df24 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AΣL(1,𝔽16), #69137, #69143, … |
| maximal normal subgroup of | D3×AΣL(1,𝔽16), #69137, #69143, … |
| maximal quotient of | #67444, #67446, #67456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 30);