Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C2×C7×#204 |
| Fitting | C2×C3×C7×C8 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×SD16 |
| Sylow | C3 ⋊ C2×C7×SD16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×#204, #13053093, #13053104, … |
| maximal normal subgroup of | Dic7×#204, #13053093, #13053104, … |
| maximal quotient of | C7×#4680, C7×#4681, C4×C7×#204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 881);