Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #1141⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#1141⋊C3 |
| unambiguous semidirect product | (C4×#1141)⋊C3 |
| Fitting | C4×C7×D4 ⋊ C2×C3 |
| Hall | C4×#1141 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C4×D8 |
| Sylow | C7 ⋊ C3×C4×D8 |
268 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 268 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 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1141⋊C3, C4×D8×AGL(1,𝔽7), C4×#6474⋊C3, … |
| maximal normal subgroup of | C4×D8×AGL(1,𝔽7), C4×#6474⋊C3, C4×#6477⋊C3, … |
| maximal quotient of | AGL(1,𝔽5)×#1141⋊C3, #72276619 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1202);