Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#88372 |
| Sylow | C27 ⋊ C2×C22⋊C4 |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13134022, #13134023, C22⋊C4×Dic27, … |
| maximal normal subgroup of | #13134022, #13134023, C22⋊C4×Dic27, … |
| maximal quotient of | C2×#11720070, #13134712, C2×C27⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 168);