Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×D24 |
| Fitting | C2×C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ C2×D8 |
544 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10589114, C3×#10589115, C3×#10589126, … |
| maximal normal subgroup of | C3×#10589114, C3×#10589115, C3×#10589126, … |
| maximal quotient of | C32×#4682, C32×C4×D24, C32×#4694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3739);