Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C32×Q16 ⋊ 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:
(1,2,5,8)(3,10,12,16)(4,13,11,7)(6,14,15,9)(20,21,22);(2,6)(3,9)(4,11)(7,16)(8,15)(10,13)(12,14)(18,19)(21,22);(17,18,19)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,c^b=cd,d^b=de39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#828, #10591038, #10591047, … |
| maximal normal subgroup of | D3×#828, #10591038, #10591047, … |
| maximal quotient of | #10589356, #10589357, #10589430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 303);