Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#67⋊C4 |
| unambiguous semidirect product | #67⋊(C3×C4) |
| Fitting | C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C4×D4 |
205 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2,3)(4,5,6)(7,10,9,8)(12,14);(11,12)(13,14);(5,6)(12,14)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10594039, #10594040, #10594048, … |
| maximal normal subgroup of | #10594039, #10594040, #10594048, … |
| maximal quotient of | C3×#4647, C3×#4649, C3×#4652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 652);