Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C26×D3 (order 384) · Inn(G) = C2×D3 · Out(G) = C25 |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D3)⋊C8 |
| unambiguous semidirect product | (C2×D3)⋊(C3×C8) |
| Fitting | C2×C32×C8 ⋊ C2 |
| Sylow | C32 ⋊ C22⋊C8 |
111 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 111 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3)(4,5,6)(8,10)(11,15,17,12,14,18,13,16);(5,6)(7,8)(9,10)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10590655, #10590656, #10590660, … |
| maximal normal subgroup of | #10590655, #10590656, #10590660, … |
| maximal quotient of | C3×#4456, C3×#4459, C3×#4468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 254);