Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#6157)⋊C32 |
| Fitting | C2×C32×C53 ⋊ C4 |
| Sylow | C53 ⋊ #7465 |
202 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,i^b=i^30,i^e=i^52992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084634);