Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | C2×#126×#6157 |
| unambiguous semidirect product | D53⋊(C4×#126) |
| Fitting | C2×#126×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×C4×#126 |
2838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114144);