Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×Dic7 |
| Hall | C3×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ C3×C4×Q8 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | Dic7×#215, #13054590, #13054592, … |
| maximal normal subgroup of | Dic7×#215, #13054590, #13054592, … |
| maximal quotient of | C3×C4⋊C4×Dic7, C3×#89753, C3×#89757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 838);