Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #2492 |
508 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|a^2=eg,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^130,c^b=cg,h^b=h^130,h^c=h^1301858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 8887);