Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic54 |
| Sylow | C27 ⋊ C4×Q8 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13133958, #13133977, C8×Dic54, … |
| maximal normal subgroup of | #13133958, #13133977, C8×Dic54, … |
| maximal quotient of | #13134153, #13134157, #13134169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 84);