Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C22×C32×Dic6 |
| Sylow | C33 ⋊ C22×Q8 |
1152 conjugacy classes of subgroups; only the 630 normal subgroups are shown.
This group has 1152 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 | C3×#10591220, C3×#10591221, C2×C3×#63560, … |
| maximal normal subgroup of | C3×#10591220, C3×#10591221, C2×C3×#63560, … |
| maximal quotient of | C2×C32×C4×Dic6, C2×C32×#869, C2×C32×#870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4610);