Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C83×#2819 ⋊ C2 |
| Sylow | C83 ⋊ #10078 |
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 97 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|d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^82,c^b=cf,d^b=dg,e^b=eh,d^c=dh,e^c=egh1100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 70847);