Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #2396 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^1302644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 7780);