Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C8×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #8240 |
522 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fgh,i^a=i^82,c^b=ch,d^b=dh3344 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 60566);