Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#1141 |
| Fitting | C2×C3×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×C3×D8 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#1141, #13054359, #13054362, … |
| maximal normal subgroup of | Dic3×#1141, #13054359, #13054362, … |
| maximal quotient of | C2×C3×#6381, C2×C3×#6383, C3×#89739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 824);