Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#379 ⋊ C4 |
| Sylow | C53 ⋊ #10935 |
2594 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 2594 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,d^a=dh,i^a=i^23,e^b=eh,f^b=fh,d^c=dh,i^c=i^30,i^f=i^52428 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092578);