Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#215 |
| Fitting | C2×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C2×SD16 |
155 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 155 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 16 points:
(3,4,5)(6,7,8)(9,10,12,14)(11,16,15,13);(4,5)(10,13)(11,15)(14,16);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10591542, Dic3×#215, #10591564, … |
| maximal normal subgroup of | #10591542, Dic3×#215, #10591564, … |
| maximal quotient of | C2×C3×#808, C2×C3×#809, C3×#4968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 712);