Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic42 |
| Hall | C3×C72 ⋊ Q8 |
| Sylow | C72 ⋊ Dic6 |
| Sylow | C3 ⋊ C7×Dic14 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72246605, D3×C7×Dic14, #72246611, … |
| maximal normal subgroup of | #72246605, D3×C7×Dic14, #72246611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 199);