Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #7177 |
238 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,c^b=ch,d^b=dh,i^b=i^822360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 56500);