Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #1132⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#1132⋊C3 |
| unambiguous semidirect product | (C4×#1132)⋊C3 |
| Fitting | C4×C7×C8 ⋊ C2×C3 |
| Hall | C4×#1132 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4×SD16 |
| Sylow | C7 ⋊ C3×C4×SD16 |
244 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1132⋊C3, C4×#6474⋊C3, C4×#6471⋊C3, … |
| maximal normal subgroup of | C4×#6474⋊C3, C4×#6471⋊C3, C4×SD16×AGL(1,𝔽7) |
| maximal quotient of | AGL(1,𝔽5)×#1132⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 880);