Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×ΓL(1,𝔽8)⋊#95 |
| unambiguous semidirect product | (C2×ΓL(1,𝔽8))⋊#95 |
| unambiguous semidirect product | (C2×C7⋊#95)⋊C3 |
| Hall | C2×C7⋊#95 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#95 |
| Sylow | C7 ⋊ C2×C3×#95 |
660 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #72228933, #72230204, #72276814, … |
| maximal normal subgroup of | #72228933, #72230204, #72276814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1397);