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×#88363 |
| 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 | #13134020, #13134025, #13134027, … |
| maximal normal subgroup of | #13134020, #13134025, #13134027, … |
| maximal quotient of | C2×#11720043, C4×#88363, C2×C4⋊(C27⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 137);