Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×(C3⋊D9)⋊Q8 |
| Sylow | C3×C9 ⋊ C22×Q8 |
522 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #13137847, #13137848, #13137851, … |
| maximal normal subgroup of | #13137847, #13137848, #13137851, … |
| maximal quotient of | #13147442, #13147443, #13147446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2427);