Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C33 |
| direct product | C2×#88859 |
| Fitting | C22×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
1848 conjugacy classes of subgroups; only the 551 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 551 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13145622, #13146013, #13160457, … |
| maximal normal subgroup of | #13145622, #13146013, #13160457, … |
| maximal quotient of | #13163567, C2×#11722175, C4×#88859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3935);