Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#1131 |
| Fitting | C2×C3×C7×C8 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×M16 |
| Sylow | C7 ⋊ C2×C3×M16 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | #13050910, C3×#89309, Dic3×#1131, … |
| maximal normal subgroup of | #13050910, C3×#89309, Dic3×#1131, … |
| maximal quotient of | C3×#89451, C3×#89457, C3×C4×#1131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 793);