Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #11869 |
364 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 72 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=e,b^2=h,c^2=gh,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=cg,d^a=df,g^a=gh,i^a=i^30,c^b=cf,d^b=dg,e^b=efgh,f^b=fh,g^b=gh,d^c=dh,i^c=i^52,e^d=eh,i^e=i^52398 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1094925);