Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88543 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#88547 |
| Sylow | C3×C9 ⋊ C2×Q16 |
300 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13140653, #13140654, #13140657, … |
| maximal normal subgroup of | #13140653, #13140654, #13140657, … |
| maximal quotient of | C2×#11720525, #13144311, C2×#11720527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1818);