Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#819 |
| Sylow | C33 ⋊ #108 |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10589120, C3×#10589122, C3×#10589126, … |
| maximal normal subgroup of | C3×#10589120, C3×#10589122, C3×#10589126, … |
| maximal quotient of | C32×#4457, C32×#4458, C32×#4552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2074);