Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63626 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C32×C16 ⋊ C2 |
| Sylow | C32 ⋊ SD32 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,7,13,12,16,3,6,5,9,10,15,4,8,11,14)(20,21,22);(2,6)(3,10)(4,12)(7,11)(8,15)(9,14)(13,16)(18,19)(21,22);(17,18,19)Polycyclic presentation:
2^5,3^2|b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,f^a=f^2,g^a=g^275 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#800, #10590232, #10590238, … |
| maximal normal subgroup of | D3×#800, #10590232, #10590238, … |
| maximal quotient of | #10589369, #10589371, #10589375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 275);