Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C9×C4⋊Dic3 |
| Sylow | C3×C9 ⋊ C2×C4⋊C4 |
330 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13135123, #13135124, #13135125, … |
| maximal normal subgroup of | #13135123, #13135124, #13135125, … |
| maximal quotient of | C2×C9×C4⋊(C3⋊C8), C9×#4924, C4×C9×C4⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1548);