Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of D144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C16 ⋊ C2 |
| Sylow | C9 ⋊ SD32 |
39 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,9,4,7,6,5,3,2,8)(10,11,16,22,21,25,12,15,14,18,19,24,13,17,20,23);(2,4)(3,7)(5,6)(8,9)(11,15)(12,19)(13,21)(16,20)(17,24)(18,23)(22,25)Polycyclic presentation:
2^5,3^2|b^2=cd,c^2=d,d^2=e,f^3=g^2,b^a=bc,c^a=cde,d^a=de,f^a=f^2g,g^a=g^275 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#63359, #10588584, #10588588, … |
| maximal normal subgroup of | C2×#63359, #10588584, #10588588, … |
| maximal quotient of | #10588180, #10588182, #10588186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 7);