Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #63545 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#63550 |
| Sylow | C33 ⋊ Q32 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10590025, C3×#10590026, #13154955, … |
| maximal normal subgroup of | C3×#10590025, C3×#10590026, #13154955, … |
| maximal quotient of | C3×#10589117, C3×#10589140, C2×C3×#63550 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1933);