Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88860 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×#88860 |
| Fitting | C2×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ C2×D8 |
1064 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 319 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #13160908, #13160909, #13160912, … |
| maximal normal subgroup of | #13160908, #13160909, #13160912, … |
| maximal quotient of | C2×#11722177, C2×#11722179, #13163626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3939);