Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88989 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4⋊(C3⋊#157) |
| Fitting | C2×C33×C4 ⋊ C4 |
| Sylow | C33 ⋊ C2×C4⋊C4 |
324 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13154806, #13154807, #13154812, … |
| maximal normal subgroup of | #13154806, #13154807, #13154812, … |
| maximal quotient of | #13173322, #13173323, #13173324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4480);