Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #26368 |
968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|a^2=f,b^2=f,c^2=f,e^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^82,c^b=cg,e^b=eh,e^d=eh2102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 232519);