Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #4245 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×(C2×D7)⋊Dic3 |
| Hall | C3×C7 ⋊ C22×C22⋊C4 |
| Sylow | C7 ⋊ C22×#217 |
| Sylow | C3 ⋊ C22×(C2×D7)⋊C4 |
1348 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 432 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 9877);