Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #21188 |
1614 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 296 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,c^2=f,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^30,c^b=ch,i^b=i^30,i^c=i^52,i^d=i^52,i^g=i^52428 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1105755);