Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #36609 |
1938 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|a^2=fh,b^2=fgh,c^2=fgh,d^2=gh,e^2=fh,b^a=bf,c^a=cg,c^b=ch,e^b=eh,d^c=dh,i^c=i^82,e^d=eh,i^e=i^822366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 375383);