Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#61451 (order 1536) · Inn(G) = #832 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #362 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,9,18)(5,10,14,27)(7,19,21,16)(8,23,24,33)(11,26,13,25)(12,29,30,31)(15,22,32,28)(17,20,34,35);(2,3)(4,5,7,11,9,14,21,13)(6,15,16,29,18,32,19,31)(8,22,20,12,24,28,35,30)(10,23,25,17,27,33,26,34)Polycyclic presentation:
2^6,3|a^2=c,b^2=f,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,c^b=cf,d^b=def,e^b=ef30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#362, #69266, #69267, … |
| maximal normal subgroup of | D3×#362, #69266, #69267, … |
| maximal quotient of | #67723, #67764, #67777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 124);