Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #3266 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|a^2=g,b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^130,d^b=de,e^b=eg,e^d=eg,h^d=h^1301654 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 16021);