Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D7×#216 |
| Hall | C3×C7 ⋊ C2×Q16 |
| Sylow | C7 ⋊ C2×#216 |
| Sylow | C3 ⋊ D7×Q16 |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#915, D7×#916, #13059314, … |
| maximal normal subgroup of | D7×#915, D7×#916, #13059314, … |
| maximal quotient of | #13052528, #13052567, #13052568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 651);