Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C2×C3×C4×#157 |
| Fitting | C2×C33×C4 ⋊ C4 |
| derived | C32 ⋊ C2×C3×C42 |
| Sylow | C33 ⋊ C2×C42 |
356 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13154793, #13154801, #13154802, … |
| maximal normal subgroup of | #13154793, #13154801, #13154802, … |
| maximal quotient of | C3×C4×#3787, C3×#10593723, C3×C4×#3788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4466);