Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4⋊(C3⋊D9) |
| Fitting | C22×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22×D4 |
1180 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 321 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 | C2×#11720267, #13139333, C2×#11720284, … |
| maximal normal subgroup of | C2×#11720267, #13139333, C2×#11720284, … |
| maximal quotient of | C2×#11721706, C2×C4×C4⋊(C3⋊D9), C2×#11721711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2620);