Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q16×D21 |
| Fitting | C3×C7×Q16 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×Q16 |
| Sylow | C7 ⋊ D3×Q16 |
| Sylow | C3 ⋊ D7×Q16 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #13053671, #13053677, #13053688, … |
| maximal normal subgroup of | #13053671, #13053677, #13053688, … |
| maximal quotient of | #13056427, #13056429, #13056431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 982);