Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D7×ΓL(1,𝔽25) |
| Fitting | C3×C7×C8 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×M16 |
| Sylow | C7 ⋊ C2×ΓL(1,𝔽25) |
| Sylow | C3 ⋊ D7×M16 |
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D7×ΓL(1,𝔽25), D7×#901, #13059179, … |
| maximal normal subgroup of | C2×D7×ΓL(1,𝔽25), D7×#901, #13059179, … |
| maximal quotient of | D7×Dic3⋊C8, #13052948, #13052952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 388);