Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#61451 (order 1536) · Inn(G) = #821 · 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)(4,6,7,19,20,31,26,32,9,16,22,15,8,17,21,35)(5,10,11,27,23,29,34,30,13,24,28,14,12,25,18,33);(2,3)(4,5,9,13)(6,14,16,27)(7,18,22,34)(8,23,20,12)(10,19,24,15)(11,26,28,21)(17,33,31,30)(25,32,29,35)Polycyclic presentation:
2^6,3|a^2=f,b^2=cd,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^2,c^b=cf,d^b=df36 conjugacy classes — view the full character table.
| maximal subgroup of | #69090, #69117, #69127, … |
| maximal normal subgroup of | #69090, #69117, #69127, … |
| maximal quotient of | #67517, #67529, #67561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 76);