Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#356 ⋊ C4 |
| Sylow | C53 ⋊ #12634 |
452 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=h,e^2=h,b^a=bd,c^a=ch,d^a=dh,f^a=fgh,i^a=i^30,d^b=dg,g^b=gh,i^b=i^23,i^c=i^30,f^d=fh,i^e=i^52,i^f=i^52215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1096135);