Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#61451 (order 1536) · Inn(G) = C2×D24 · Out(G) = C24 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #510 |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(4,7,16,31,17,19,8,20,9,21,28,34,6,15,23,35)(5,11,26,32,10,24,12,18,14,27,22,30,13,25,29,33);(4,6,9,17)(5,10,14,13)(7,19,21,15)(8,16,23,28)(11,25,27,24)(12,22,29,26)(18,32,33,30)(20,34,35,31);(2,3)(4,5)(6,10)(7,18)(8,22)(9,14)(11,20)(12,28)(13,17)(15,30)(16,29)(19,32)(21,33)(23,26)(24,31)(25,34)(27,35)Polycyclic presentation:
2^6,3|b^2=f,c^2=de,d^2=e,e^2=f,c^a=cd,d^a=def,e^a=ef,g^a=g^2,c^b=cf36 conjugacy classes — view the full character table.
| maximal subgroup of | #69090, #69121, #69128, … |
| maximal normal subgroup of | #69090, #69121, #69128, … |
| maximal quotient of | #69069, #69077, #69079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 468);