Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#324 ⋊ C4 |
| Sylow | C53 ⋊ #7322 |
338 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 52 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=d,b^2=e,c^2=h,d^2=f,b^a=bc,c^a=cf,e^a=egh,i^a=i^23,c^b=cg,d^b=dfh,g^b=gh,i^b=i^30,e^c=eh,i^d=i^52,i^e=i^52320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084314);