Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#89019 |
| Sylow | C33 ⋊ C22×Q8 |
1152 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #13155336, #13155366, #13155418, … |
| maximal normal subgroup of | #13155336, #13155366, #13155418, … |
| maximal quotient of | #13175132, #13175135, #13175137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4535);