Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#33551 (order 1536) · Inn(G) = #834 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| 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)(5,8)(6,11)(9,10);(2,3)(4,5)(6,9,11,8)(7,10)Polycyclic presentation:
2^6,3|a^2=c,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,c^b=ce,d^b=df,d^c=df27 conjugacy classes — view the full character table.
| maximal subgroup of | #67462, #67539, #67540, … |
| maximal normal subgroup of | #67462, #67539, #67540, … |
| maximal quotient of | #67635, #67640, #67641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 104);