Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C22×C3×Dic14 |
| Hall | C3×C7 ⋊ C22×Q8 |
| Sylow | C7 ⋊ C22×C3×Q8 |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 672 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | #13053692, #13053693, C2×#10620496, … |
| maximal normal subgroup of | #13053692, #13053693, C2×#10620496, … |
| maximal quotient of | C2×C3×C4×Dic14, C2×C3×#6432, C2×C3×#6433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1203);