Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C4×#638 |
| Fitting | C22×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C4×D4 |
780 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10591148, C3×#10591149, C3×#10591157, … |
| maximal normal subgroup of | C3×#10591148, C3×#10591149, C3×#10591157, … |
| maximal quotient of | C3×C4×#3750, C3×#10592632, C3×C4×#3752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3850);