Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×#217 |
| Sylow | C32 ⋊ C2×C22⋊C4 |
331 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 130 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)(9,10)(11,12)(13,14)(15,16);(4,5)(10,12)(13,14,15,16);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10589186, #10589187, C3×#4526, … |
| maximal normal subgroup of | #10589186, #10589187, C3×#4526, … |
| maximal quotient of | C2×C3×#830, C3×#5207, C2×C3×C3⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 723);