Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic21 |
| Hall | C3×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ Q8×Dic3 |
| Sylow | C3 ⋊ Q8×Dic7 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13054602, #13054603, #13054604, … |
| maximal normal subgroup of | #13054602, #13054603, #13054604, … |
| maximal quotient of | C4⋊C4×Dic21, #13056612, #13056616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1010);