Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×C3⋊#95 |
| unambiguous semidirect product | C3⋊(C3×#95) |
| Sylow | C32 ⋊ #95 |
179 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 90 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)(11,14,13,12)(16,18);(5,6)(7,10,9,8)(15,16)(17,18)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10589149, #10589151, #10589153, … |
| maximal normal subgroup of | #10589149, #10589151, #10589153, … |
| maximal quotient of | C3×#4523, C3×#4524, C3×#4526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 265);