Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#66728 |
| Fitting | C23×C3×C4×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ C22×#41 |
| Sylow | C7 ⋊ C22×#235 |
| Sylow | C3 ⋊ C22×#1157 |
1780 conjugacy classes of subgroups; only the 619 normal subgroups are shown.
This group has 1780 conjugacy classes of subgroups — too many to draw. Only its 619 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11660);