Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×C4×#611 |
| Fitting | C22×C3×C4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C4×D4 |
336 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 116 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⋊C8×#611, #13139480, #611⋊(C3⋊C8), … |
| maximal normal subgroup of | C3⋊C8×#611, #13139480, #611⋊(C3⋊C8), … |
| maximal quotient of | C3×C4×Dic9⋊C4, C3×#10588613, C3×C4×(C2×D9)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1551);