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) = C2×C4 |
No aliases for this group.
| Fitting | C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #353 |
86 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)(6,8,10,11)(7,9);(2,3)(5,8)(6,10)(9,11)Polycyclic presentation:
2^6,3|b^2=c,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^2,d^b=def,e^b=ef,d^c=df24 conjugacy classes — view the full character table.
| maximal subgroup of | #69130, #69133, #69139, … |
| maximal normal subgroup of | #69130, #69133, #69139, … |
| maximal quotient of | #67448, #67451, #67453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 33);