Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #137 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,5,7,9,8,3,6,4)(11,16)(12,19)(13,21)(15,22)(17,18)(23,24);(10,12)(11,15)(13,20)(14,19)(16,24)(17,22)(18,23)(21,25);(2,4)(3,7)(5,6)(8,9)(10,11,14,18)(12,15,19,23)(13,16,21,17)(20,24,25,22)Polycyclic presentation:
2^5,3^2|a^2=e,d^2=e,f^3=g^2,c^a=cd,d^a=de,f^a=f^2g,g^a=g^2,c^b=ce,d^c=de51 conjugacy classes — view the full character table.
| maximal subgroup of | #10588505, #10588506, #10588821, … |
| maximal normal subgroup of | #10588505, #10588506, #10588821, … |
| maximal quotient of | #10588679, #10588680, #10588681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 159);