Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×C4×C3⋊#157 |
| Fitting | C2×C33×C4 ⋊ C4 |
| derived, Sylow | C33 ⋊ C2×C42 |
356 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #13154794, #13154799, #13154803, … |
| maximal normal subgroup of | #13154794, #13154799, #13154803, … |
| maximal quotient of | C4×#88988, #13173320, C4×#88989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4479);