Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#3710 |
| derived | C32 ⋊ C22×C3×C8 |
| Sylow | C33 ⋊ C22×C8 |
418 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590043, C3×#10590044, C3×#10590049, … |
| maximal normal subgroup of | C3×#10590043, C3×#10590044, C3×#10590049, … |
| maximal quotient of | C3×#10590254, C3×#10590256, C3×#10590297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3108);