Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C33 |
| direct product | C4×#6312 |
| Fitting | C22×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C4×D4 |
1316 conjugacy classes of subgroups; only the 383 normal subgroups are shown.
This group has 1316 conjugacy classes of subgroups — too many to draw. Only its 383 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 | #13160712, #13160713, #13160718, … |
| maximal normal subgroup of | #13160712, #13160713, #13160718, … |
| maximal quotient of | C4×#88857, #13163571, C4×#88859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3936);