Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ #99 |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 14 points:
(4,5,6)(7,9)(8,11,12,13)(10,14);(2,3)(5,6)(7,8)(9,13)(10,12)(11,14);(1,2,3)Polycyclic presentation:
2^5,3^2|b^2=c,b^a=bd,c^a=ce,f^a=f^2,g^a=g^2,d^b=de51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#806, #10590405, #10590407, … |
| maximal normal subgroup of | D3×#806, #10590405, #10590407, … |
| maximal quotient of | #10589317, #10589318, #10589333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 281);