Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C727 ⋊ C2 |
| Sylow | C727 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5816 |
Polycyclic presentation:
2^5,727|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^726,d^b=de,f^b=f^7263641 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 174);