Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C53×#396 ⋊ C4 |
| Sylow | C53 ⋊ #14331 |
1290 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1290 conjugacy classes of subgroups — too many to draw. Only its 230 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=h,b^2=f,d^2=fgh,b^a=be,c^a=cf,i^a=i^23,c^b=cg,d^c=de,i^d=i^30,i^h=i^52350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098826);