Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C4×C3⋊D9 |
| Fitting | C22×C3×C4×C9 ⋊ C2 |
| derived, Sylow | C3×C9 ⋊ C23×C4 |
1180 conjugacy classes of subgroups; only the 361 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 361 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720282, #13139396, #13139487, … |
| maximal normal subgroup of | C2×#11720282, #13139396, #13139487, … |
| maximal quotient of | C2×C4×#6226, C2×C42×C3⋊D9, C2×#11721709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2619);