Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D727)⋊C8 |
| Fitting | C2×C8×C727 ⋊ C2 |
| Sylow | C727 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
Polycyclic presentation:
2^5,727|a^2=d,d^2=e,b^a=bc,f^b=f^7265828 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 58);