Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#64241 |
| Fitting | C22×C33 ⋊ D4 |
| Sylow | C33 ⋊ #120 |
496 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | #13165567, #13165568, C3×#10593414, … |
| maximal normal subgroup of | #13165567, #13165568, C3×#10593414, … |
| maximal quotient of | C3×#10593398, C3×#10593401, C3×#10593402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4263);