Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×#812 |
| Sylow | C33 ⋊ M32 |
244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10589105, C3×#10589106, C3×#10589109, … |
| maximal normal subgroup of | C3×#10589105, C3×#10589106, C3×#10589109, … |
| maximal quotient of | C32×#4461, C32×C4⋊(C3⋊C16), C32×#4549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2067);