Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C22×C3×Q8) |
| Fitting | C22×C7×Q8 ⋊ C2×C3 |
| Hall | C22×Q8×D7 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C23×Q8 |
| Sylow | C7 ⋊ C23×C3×Q8 |
1700 conjugacy classes of subgroups; only the 928 normal subgroups are shown.
This group has 1700 conjugacy classes of subgroups — too many to draw. Only its 928 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#41×AGL(1,𝔽7) |
| maximal normal subgroup of | C22×#41×AGL(1,𝔽7) |
| maximal quotient of | AGL(1,𝔽7)×#543 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11437);