Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#1143 |
| Fitting | C2×C3×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×SD16 |
| Sylow | C7 ⋊ C2×C3×SD16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#1143, #13054599, #13054602, … |
| maximal normal subgroup of | Dic3×#1143, #13054599, #13054602, … |
| maximal quotient of | C2×C3×#6382, C2×C3×#6383, C3×#89740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 834);