Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63385 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×Q16 ⋊ 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)(10,11,14,17)(12,19,21,25)(13,22,20,16)(15,23,24,18);(2,4)(3,7)(5,6)(8,9)(11,15)(12,18)(13,20)(16,25)(17,24)(19,22)(21,23)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=de,d^2=e,f^3=g^2,b^a=bc,c^a=cd,d^a=de,f^a=f^2g,g^a=g^2,c^b=cd,d^b=de39 conjugacy classes — view the full character table.
| maximal subgroup of | D9×SD32, #10588594, #10588598, … |
| maximal normal subgroup of | D9×SD32, #10588594, #10588598, … |
| maximal quotient of | #10588167, #10588168, #10588241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 35);