Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#89040 |
| Sylow | C33 ⋊ C22×Q8 |
770 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #13155335, #13155364, #13155365, … |
| maximal normal subgroup of | #13155335, #13155364, #13155365, … |
| maximal quotient of | #13178111, #13178114, C4×#89040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4579);