Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C83×#1812 ⋊ C2 |
| Sylow | C83 ⋊ #29155 |
608 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2656 |
Polycyclic presentation:
2^8,83|a^2=efg,b^2=eg,d^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,c^b=cg,d^b=dh,i^b=i^82,g^c=gh1352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 269528);