Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#819 |
| Sylow | C3×C9 ⋊ #108 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13135001, #13135002, #13135003, … |
| maximal normal subgroup of | #13135001, #13135002, #13135003, … |
| maximal quotient of | C9×#4457, C9×#4458, C9×#4552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 381);