Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C32×D12 |
| Fitting | C22×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C22×D4 |
1632 conjugacy classes of subgroups; only the 630 normal subgroups are shown.
This group has 1632 conjugacy classes of subgroups — too many to draw. Only its 630 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 | C2×C3×#63558, C2×C3×#63562, C2×C3×#63563, … |
| maximal normal subgroup of | C2×C3×#63558, C2×C3×#63562, C2×C3×#63563, … |
| maximal quotient of | C2×C32×#869, C2×C32×C4×D12, C2×C32×#874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4612);