Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ AGL(1,ℤ/8) |
204 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3,5,4,6,7,8)(12,13,14);(2,6)(5,8)(9,10,11);(2,5)(3,7)(6,8)(10,11)(13,14)Polycyclic presentation:
2^5,3^2|c^2=d,d^2=e,c^a=cd,d^a=de,f^a=f^2,g^a=g^2,c^b=ce51 conjugacy classes — view the full character table.
| maximal subgroup of | #10590987, #10590990, #10591015, … |
| maximal normal subgroup of | #10590987, #10590990, #10591015, … |
| maximal quotient of | #10592401, #10592409, #10592410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 765);