Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#235 |
| Fitting | C22×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C2×#41 |
355 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 355 conjugacy classes of subgroups — too many to draw. Only its 178 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 — 4 generators on 16 points:
(1,2)(3,4,5)(6,7,8)(10,14)(13,16);(9,11,12,15)(10,13,14,16);(4,5)(9,10)(11,13)(12,14)(15,16);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10591070, #10591071, #10591076, … |
| maximal normal subgroup of | #10591070, #10591071, #10591076, … |
| maximal quotient of | C2×C3×C4×Dic6, C2×C3×#870, C3×#5470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 991);