Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C9×M16 ⋊ C2 |
| Sylow | C9 ⋊ #100 |
69 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,6,8,7,2,4,3,9,5)(10,11,12,15,13,14,16,17);(2,4)(3,7)(5,6)(8,9)(11,14)(12,16)Polycyclic presentation:
2^5,3^2|b^2=c,c^2=e,f^3=g^2,b^a=bd,c^a=ce,f^a=f^2g,g^a=g^2,d^b=de51 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#100, #10588429, #10588431, … |
| maximal normal subgroup of | D9×#100, #10588429, #10588431, … |
| maximal quotient of | #10588142, #10588146, #10588158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 31);