Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C32×#216 |
| Sylow | C33 ⋊ C2×Q16 |
512 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 512 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 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic3×#216, C3×#10591574, C3×#10591576, … |
| maximal normal subgroup of | C3×Dic3×#216, C3×#10591574, C3×#10591576, … |
| maximal quotient of | C32×#4970, C2×C32×#807, C2×C32×#810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3779);