Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×Q8×C3⋊D9 |
| Fitting | C2×C3×Q8×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22×Q8 |
780 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13140713, #13140722, #13140733, … |
| maximal normal subgroup of | #13140713, #13140722, #13140733, … |
| maximal quotient of | C2×#11721743, C2×#11721752, C2×#11721744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2632);