Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C509 ⋊ C2 |
| Sylow | C509 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4072 |
Polycyclic presentation:
2^6,509|b^a=bd,c^a=ce,g^a=g^508,e^b=ef,d^c=df4334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 736);