Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D727)⋊C4 |
| Fitting | C22⋊C4×C727 ⋊ C2 |
| Sylow | C727 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
Polycyclic presentation:
2^5,727|a^2=e,c^2=e,b^a=bd,f^c=f^7263650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 106);