Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#88359 |
| Fitting | C2×C8×C27 ⋊ C2 |
| Sylow | C27 ⋊ C2×M16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13134011, C4×#88359, #13134195, … |
| maximal normal subgroup of | #13134011, C4×#88359, #13134195, … |
| maximal quotient of | #13134184, #13134192, C4×#88359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 117);