Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | #379×#6157 |
| Fitting | C53×#379 ⋊ C4 |
| Sylow | C53 ⋊ C4×#379 |
6734 conjugacy classes of subgroups; only the 640 normal subgroups are shown.
This group has 6734 conjugacy classes of subgroups — too many to draw. Only its 640 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 848 |
476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098199);