Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #611⋊C4 |
| Fitting | C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ C4×D4 |
141 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,6,8,7,2,4,3,9,5)(10,11,12,13)(15,17);(14,15)(16,17);(2,4)(3,7)(5,6)(8,9)(15,17)Polycyclic presentation:
2^5,3^2|c^2=d,f^3=g^2,b^a=be,f^a=f^2g,g^a=g^2,c^b=ce60 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#611⋊C4, #10589588, #10589592, … |
| maximal normal subgroup of | C2×#611⋊C4, #10589588, #10589592, … |
| maximal quotient of | #10588327, #10588329, #10588332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 91);