Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #7304 |
764 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 62 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=d,b^2=e,b^a=bc,c^a=cf,e^a=eg,f^a=fh,i^a=i^30,c^b=cg,d^b=df,d^c=dh,i^d=i^52554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084270);