Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C727 ⋊ C2 |
| Sylow | C727 ⋊ #135 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
Polycyclic presentation:
2^5,727|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^726,d^b=de,f^b=f^7265822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 168);