Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63745 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#63748 |
| Sylow | C33 ⋊ #108 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10593167, C3×#10593168, C3×#10593169, … |
| maximal normal subgroup of | C3×#10593167, C3×#10593168, C3×#10593169, … |
| maximal quotient of | C3×#10590088, C3×#10590089, C3×#10590097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2769);