Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #10648 |
236 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 67 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=eh,b^2=g,c^2=d,d^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^82,c^b=cf,d^b=dg,e^b=eg,f^b=fh,i^b=i^82,e^c=eh,f^c=fgh1097 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 74472);