Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×#20291216 |
| unambiguous semidirect product | D53⋊#2337 |
| Fitting | C2×#124×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#2337 |
3046 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114191);