Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #157⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#157⋊D3 |
| Fitting | C33×C4 ⋊ D4 |
| Sylow | C33 ⋊ C4×D4 |
328 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #13165106, #13165124, #13165174, … |
| maximal normal subgroup of | #13165106, #13165124, #13165174, … |
| maximal quotient of | C8×#157⋊D3, #13167358, #13167359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4309);