Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#10596842 |
| unambiguous semidirect product | (C2×#10596842)⋊C22 |
| Fitting | C23×C73 ⋊ C8 |
| Sylow | C73 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 584 |
112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 1660);