Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #23612 |
1214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=ef,b^2=e,d^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,c^b=cg,i^b=i^82,d^c=dh,e^c=eh,f^c=fh,g^c=gh1856 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 198209);