Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#381 ⋊ C4 |
| Sylow | C53 ⋊ #10938 |
1234 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1234 conjugacy classes of subgroups — too many to draw. Only its 170 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=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^52,d^b=dh,e^b=eh,f^b=fh,i^b=i^30,d^c=dh,i^g=i^52422 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092584);