Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×M16 ⋊ C2 |
| 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)(10,13,14,21,15,22,12,19)(11,17,16,20,18,25,23,24);(10,12,15,14)(11,16,18,23)(13,21,22,19)(17,24,25,20);(2,4)(3,7)(5,6)(8,9)(10,11)(12,16)(13,20)(14,23)(15,18)(17,21)(19,25)(22,24)Polycyclic presentation:
2^5,3^2|b^2=e,c^2=d,d^2=e,f^3=g^2,c^a=cd,d^a=de,f^a=f^2g,g^a=g^2,c^b=ce51 conjugacy classes — view the full character table.
| maximal subgroup of | #10588426, #10588428, #10588432, … |
| maximal normal subgroup of | #10588426, #10588428, #10588432, … |
| maximal quotient of | #10588382, #10588383, #10588384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 119);