Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#213 |
| Fitting | C2×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C2×D8 |
179 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 179 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) = 48 |
A minimal faithful permutation representation — 3 generators on 16 points:
(3,4,5)(6,7,8)(10,13)(11,16)(14,15);(4,5)(9,10)(11,13)(12,15)(14,16);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10591406, Dic3×#213, #10591428, … |
| maximal normal subgroup of | #10591406, Dic3×#213, #10591428, … |
| maximal quotient of | C2×C3×#807, C2×C3×#809, C3×#4967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 702);