Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C2×C4⋊(D7⋊A4) |
| unambiguous semidirect product | (C2×D28)⋊A4 |
| Fitting | C23×C4×C7 ⋊ C2×C3 |
| Hall | C23×D28 ⋊ C3 |
| Sylow | C7 ⋊ C2×D4×A4 |
634 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11473);