Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×C4×Dic6 |
| Sylow | C32 ⋊ C4×Q8 |
155 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 155 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 — 3 generators on 18 points:
(1,2,3)(4,5,6)(11,18,14,13)(12,17,16,15);(5,6)(11,16,14,12)(13,15,18,17);(7,10,9,8)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10589083, #10589084, C3×#4456, … |
| maximal normal subgroup of | #10589083, #10589084, C3×#4456, … |
| maximal quotient of | C3×#4646, C3×#4647, C3×#4654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 639);