Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C22⋊C8 |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,3,6)(2,5,4)(8,10)(11,13,15,14)(12,16,18,17);(1,2)(3,5,6,4)(7,8)(9,10)(11,12,14,17,15,18,13,16)Polycyclic presentation:
2^5,3^2|a^2=c,b^2=e,c^2=e,b^a=bd,f^a=fg^2,g^a=f^2g^2,f^c=f^2,g^c=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10590027, #10590028, #10590157, … |
| maximal normal subgroup of | #10590027, #10590028, #10590157, … |
| maximal quotient of | #10590160, #10590161, #10590176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 426);