Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C32×ΓL(1,𝔽25) |
| Fitting | C2×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ C2×M16 |
496 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10589109, #13145554, C32×#4514, … |
| maximal normal subgroup of | C3×#10589109, #13145554, C32×#4514, … |
| maximal quotient of | C32×#4679, C32×#4685, C32×C4×ΓL(1,𝔽25), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3736);