Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic27⋊C4 |
| Sylow | C27 ⋊ C2×C4⋊C4 |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13133963, #13134152, #13134153, … |
| maximal normal subgroup of | #13133963, #13134152, #13134153, … |
| maximal quotient of | C4×Dic27⋊C4, #13134439, #13134447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 139);