Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C9×#213 |
| Fitting | C2×C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×D8 |
282 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | #13140369, #13140374, #13140377, … |
| maximal normal subgroup of | #13140369, #13140374, #13140377, … |
| maximal quotient of | C2×C9×#807, C2×C9×#809, C9×#4967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1583);